• Supports a range of expiry definitions (tenor-based, listed, or custom date/time).
• Offers multiple strike scales (strike, moneyness, log-moneyness, delta call/put, or FX-style).

Transitioning from implied volatility to actual pricing requires the same versatile API—offering possibility to calculate these with different premium conventions (especially in FX or digital assets). In this post, we explore how to streamline pricing by:

• Allowing configurable premium conventions (for example, paying the premium in a chosen currency), and
• Defining preset payoffs that let users retrieve implied volatility, pricing, and risk metrics for multiple structures (European vanilla, digitals, risk reversals, strangles, ...) in one request.

Today, our focus is on European vanilla options as a straightforward example. The same method applies to more complex payoffs, which we’ll cover in future blogs.

Options on Futures, Inverse Payouts in Digital Assets, and Premium Conventions

In the digital asset options market, it is common for options to be written on futures rather than the underlying spot price, although the difference is generally not material as we discuss below. Settlement currencies may be "foreign" in FX terms (e.g. BTC) or domestic (e.g. USDC). For example, settling a BTCUSD option in BTC avoids direct USD exposure, while options on altcoins like XRP/USDC are typically settled in USDC—a digital asset pegged to USD. Below, we explain how these structures work and why they matter to traders. In general, exchange-traded options follow specific settlement and premium conventions; however, with a flexible API, users can also price and calculate risk for OTC (over-the-counter) options that are not exchange traded.

Reminder: Call, Put, and Inverse Options​

A call option grants the holder the right—but not the obligation—to buy the underlying asset at a predetermined strike price at (or before) expiry, while a put option grants the holder the right to sell. For standard "vanilla" options, the payoffs at expiry are defined as:

• Call payoff: max(S − K, 0)
• Put payoff: max(K − S, 0)

Here, S represents the underlying asset's price (spot or futures) at expiry, and K is the strike price.

In the cryptocurrency market—such as BTC/USD—options may also be structured as "inverse," a term specific to crypto. In traditional FX markets, these are simply described as options settled in the foreign currency. For instance, in a BTC/USD pair, BTC is considered the "foreign" currency and USD the "domestic." Thus, an inverse option on BTC/USD settles in BTC rather than USD. This structure avoids USD cash exchange at maturity and can simplify regulatory considerations.

The payoffs for inverse options at expiry are:

• Inverse Call payoff: max(S − K, 0) / S
• Inverse Put payoff: max(K − S, 0) / S

In this context, S is the USD price of BTC at expiry, and the payoff is denominated directly in BTC. Although the underlying asset is often quoted as the spot price, these options typically reference future prices expiring at the same time as the option itself.

After properly adjusting for discount factors and changing numeraires (the reference currency for valuation), inverse options become economically similar to their standard (linear) counterparts. In other words, when accounting for the time value and currency conversions, inverse and linear options exhibit identical economic characteristics and risk-return profiles.

Options on Futures​

In the digital asset options market, particularly for Bitcoin, options are usually written on futures contracts rather than directly on the BTCUSD spot price. These futures are linked to an index aggregating prices from multiple exchanges and aren't generally tradable themselves. Options typically inherit expiry dates and attributes from these underlying futures, adding complexity due to indirect linkage to the spot price via futures and indices.

However, because digital asset options and futures typically share expiry dates, this indirect relationship has minimal practical impact. At expiry, futures prices converge with the underlying index price, aligning option values with their intrinsic index-based values.

Unlike commodities, where options and underlying futures often have mismatched expiry dates, crypto markets commonly align these expirations. Additionally, platforms like Deribit calculate settlement prices by averaging the underlying index price over a 30-minute window before expiry, reducing manipulation risk and ensuring fairness.

Cash Settlement​

Most digital asset options are cash-settled, meaning that at expiry you receive (or pay) the net "cash value" in either currency X or Y (for X/Y options). For example, BTC/USD options typically settle in BTC, while SOL/USDC options settle in USDC. Cash settlement avoids the logistical complexities associated with "physically" delivering multiple currency flows.

• Physically Settled: This method involves exchanging the underlying asset (e.g., BTC for USD or vice versa) at the strike price upon expiry. Physical settlement is less common in crypto markets but is standard practice in many FX markets.
• Cash Settled: With cash settlement, the difference between the option’s payoff and the strike price is paid out directly in BTC or USD. This approach is generally preferred due to its simplicity, provided the settlement procedure remains consistent and transparent.

Premium Conventions​

Exchanges often use specific premium conventions, but multiple possibilities exist for expressing premiums, particularly within FX markets. Typically, FX traders use different premium conventions depending on the currency pairs traded.

With Qytrees API, beyond selecting the asset for final settlement (e.g., BTC vs. USD), users can also choose how the option premium is quoted. Similar to FX markets—where a call option’s premium can be expressed in either the domestic or foreign currency—our API supports several premium conventions, represented through the PremiumConvention enum. These conventions are inspired by FX market practices, offering flexibility in how premiums are interpreted and reported.

We will cover the detailed mapping of these conventions, along with practical examples, in an upcoming blog post.

• QUOTE_ASSET: Premium denominated in the “quote” (domestic) currency.
• BASE_ASSET_PERCENTAGE: Premium denominated in the “base” (foreign) currency (e.g., paying in BTC for BTC/USD options). Usually referred to as percentage foreign in FX.
• QUOTE_ASSET_PERCENTAGE and BASE_ASSET are more generally used in FX markets rather than digital assets markets, and commonly known as percentage domestic and foreign pips respectively.
• UNDISCOUNTED_...: These represent the same conventions but exclude discount factors, enabling pricing in terms of undiscounted amounts or percentages.

By treating either asset as the numeraire, these conventions allow users to incorporate multiple quoting styles within a consistent framework,

The payoff node​

Qytrees API leverages GraphQL, offering several advantages as discussed in our previous blog. GraphQL allows you to precisely define your requirements by specifying each node and subnode. We've already explored how to define the strike and expiry nodes. Below, we will discuss the payoff node that applies to each strike and expiry.

For instance, a user can specify a range of strikes in Moneyness between 0.9 and 1.1 with increments of 0.1, along with a list of expiries in tenor format such as 1M, 6W:

strike:{
  selection: null
  strikeType:{scale: MONEYNESS}
  range: [0.9, 1.1, 0.1]
}
expiry:{
  selection: null
  list: ["1M", "6W"]
}

For each strike and expiry combination, the payoff node assigns a payoff type.

The payoff node consists of two subnodes: Selection and List described below.

• Selection: Using the selection subnode, a user can choose for example "LISTED," which includes all payoffs available from the selected source.
• List: With the List subnode, a user can explicitly define the desired payoff types. For example, the user below specifies two payoff types: a vanilla call and a vanilla put. This means that for each of the defined strikes and expiries, both of these payoffs will be generated.

While many other payoff structures are supported, this section focuses specifically on vanilla options:

 payoff:
    {
      selection: null
      list : [
        {vanilla:{callPut: CALL}}
      	{vanilla:{callPut: PUT}}
      ]
    }

Output Nodes​

The previously discussed nodes—strike, expiry, and payoff—form part of the input portion of the GraphQL query, enabling precise control over what the user wants to analyze. Once the inputs are defined, the output section determines what information is retrieved in response to the query.

In this blog, we focus on the Price Node, one of several available output nodes.

Price Node​

The price node, together with your selected premium convention and payoff structure, allows the API to compute option prices.

Below is an example using GraphQL aliases to retrieve prices using two different premium conventions simultaneously:

 quote_price: price(premiumConvention: QUOTE_ASSET) {
  mid
}

quote_price_percentage: price(premiumConvention: QUOTE_ASSET_PERCENTAGE) {
  mid
}

In this example, quote_price and quote_price_percentage are aliases. They enable users to query the same field (price) multiple times with different arguments, without conflicts in the GraphQL response. Here, the user is requesting prices using two different premium conventions for all strikes, expiries, and payoffs defined in the input.

A Practical Example​

Say you want to price a 3-month BTC/USD At-The-Money Zero-Delta Straddle, where the premium is expressed in BTC. This can be configured in a single request using the API.

In future blog entries, we’ll explore additional output nodes, including:

• Implied Volatility Node – returns the full IV surface or selected slices.
• Risk Node – provides option Greeks and sensitivity metrics.

These modular output fields give users fine-grained control over the structure and granularity of the returned data.

Conclusion

This blog highlights the flexibility of the API, allowing users to build custom queries and request data of completely different nature—all within a single request.

We’ll explore additional data types and features in future posts.

If you have a specific use case or topic you'd like us to cover, feel free to reach out.

Reminder: Why Implied Volatility?

Options grant holders the right (but not the obligation) to buy or sell an underlying asset at a specific strike on or before a certain date. Factors like the forward price, strike, maturity, and interest rates make raw option prices vary widely across assets, tenors or strikes. For example the price of a 1 month call option At the Money Forward strike for BTC/USD is as of writing of this blog around 5000 USD whereas for ETH/USD the price is around 150 USD.

Implied volatility (IV) simplifies this comparison by “reverse-engineering” volatility from the price using the Black–Scholes model. When plotted against strike, IV often forms a U-shaped (convex) volatility smile, shaped by market perceptions of risk (e.g., more demands for OTM puts in bear markets or OTM calls in bullish ones) and hedging strategies. Because IV is standardized, traders can compare options more directly—then convert IV back to a price when needed by using the BS pricing machinery.

A consistent volatility smile is central to pricing more complex products and managing risk. (Check out our other posts here for in-depth discussions.)

Several Key Scales for the Vol Smile

Moneyness Definition​

Moneyness = Strike / Forward

Rationale: Normalizes the strike relative to the forward price, simplifying comparisons across underlyings and maturities.

Log-Moneyness Definition​

Log-Moneyness = Log(Strike / Forward)

Benefit: Creates a more symmetric shape around at-the-money, aligning better with certain pricing models.

Delta-Based Delta Range​

Calls typically span 0%–100%, while puts run –100%–0%.

Why It’s Useful: Plotting IV vs. delta (e.g., a “25-delta call”) is a common practice in FX and crypto, yielding a uniform yardstick across underlyings.

Different Delta Definitions: Market convention in FX vary by currency pair and sometimes by maturity (We’ll explore these in another post). In the crypto market, such conventions are not yet considered but FX Traders view can be applied on crypto as well.

Delta Call​

Delta Put​

FX Style representation of the Volatility smile​

FX-Inspired Conventions: Traders often track 2, 5, 10, or 25 delta calls/puts at various maturities. Platforms like Bloomberg provide direct comparisons for these standard deltas.

ATM Variations: “At-the-money” may be forward-based or delta-neutral (DN). FX markets often prefer DN.

Streamlining Data Retrieval with an Adaptable API

Traditionally, retrieving volatilities or strikes for a specific convention can mean juggling forward prices, discount curves, or iterative solvers—especially under multiple delta definitions (premium-adjusted vs. spot, etc.). With Qytrees’ GraphQL-powered API, you can:

• When using delta call or delta put or fx style specify Your delta Convention**: Premium-adjusted, forward, spot, etc.
• Any Delta (e.g., a 23-delta put)
• Or choose any values for your chosen scales (exemple log-moneyness or strikes).
• Input the strikes in the scale that is suitable for you — or reverse it: give a strike, retrieve its delta or vice versa.

Key Benefits​

• Request Exactly What You Need: Pull vol data for particular tenors, strikes, or deltas in a single request.
• Compare Scales: Pivot between strike-based, moneyness-based, log-moneyness-based, and delta-based quoting without extra queries.
• Focus on Analysis: Minimize tedious computations and emphasize market insights.
• Build a Vol Matrix: Easily create custom volatility grids for any maturity, strike, or delta convention.
• Vectorized & Parallel Computations: Fetch multiple maturities or valuation dates—in different time zones or cutoffs—just as quickly as for a single date.
• Parallel computation for valuation dates – allows you to do historical analysis in a smooth way by defining the range of historical data and the observation frequency

Qytrees' GraphQL Basics for Option Analytics​

Qytrees' GraphQL endpoint allows you to build custom queries around a predefined schema. For option data, you typically define:

• baseAsset and quoteAsset
• An expiry node (to choose tenors, explicit dates, or listed exchange expiries)
• A strike node (to choose scale, moneyness, or delta conventions)
• Optional additional nodes (e.g., a payoff node for pricing) will be discussed in upcoming blogs.

Defining Expiries in One Node​

The expiry node is especially powerful in Qytrees. Common use cases include:

• Tenor-Based An example below:

expiry: {
  list: ["1M", "2M", "7W2D"],
  cutTime: "8AM"
}

Specify rolling tenors (like 1M, 2M), and optionally set a cutTime (e.g., 8 AM). If cutTime is omitted, the system uses rolling tenors relative to the valuation date/time.

• Explicit Dates

expiry: {
  list: ["21/04/2025 08:30", "21/06/2025 12:30"]
}

Provide exact date/times. If you omit times or cutTime, a default cutoff is used similar to listed option from the same data soure.

• Listed Exchange Expiries

expiry: {
  selection: LISTED
}

Pulls only exchange-listed expiry dates (e.g., from Deribit).

By customizing expiry, you can retrieve precisely the volatility data you need—whether you’re after standard tenors, fixed calendar dates, or exchange-specific listings.

Controlling the Strike Node​

Similarly, the strike node defines how you set or retrieve strikes:

• Delta Convention Example

strike: {
    strikeType: {
        scale: DELTA_CALL
        deltaConvention: FORWARD
    },
    list: [0.12, 0.133, 0.543, 0.65]
}

This example node allows you to request strikes at specific call delta levels using a forward-based delta convention.

• Log-Moneyness Range

strike: {
  strikeType: {
    scale: LOG_MONEYNESS
  },
  range: [-1, 1.5, 0.1]
}

Here, you define a range for log-moneyness from –1 to 1.5 in increments of 0.1.

• FX-Style Delta

strike: {
  strikeType: {
    scale: FX_STYLE,
    deltaConvention: SPOT
  },
  list: ["2P", "4P", "12P", "27P", "35P", "DNS", "25C", "10C", "5C"]
}

This approach follows an FX-style definition, specifying deltas such as “2P” (2-delta put) or “25C” (25-delta call). DNS refers to a Delta Neutral Straddle.

• Listed Strikes

strike: {
  selection: LISTED
}

Fetches only strikes actively listed on your chosen exchange.

As shown, Qytrees supports a broad range of strike and expiry definitions, enabling direct access to both standard and more specialized quoting styles.

Conclusion

Implied volatility makes comparing options across diverse strikes, maturities, and underlyings more efficient. Whether you prefer moneyness, log-moneyness, or delta-based quoting, the critical decision is choosing a scale that fits your trading or research goals. With Qytrees’ flexible GraphQL API, you can:

• Define expiries in a single node (tenors, explicit dates, or listed calendars)
• Seamlessly request vol data in any scale—strike, moneyness, log-moneyness, or delta
• Stay focused on insights, risk, and strategy rather than data wrangling

Stay tuned for upcoming posts covering term structure, skew, and other advanced methods of analyzing volatility surfaces!

If you have specific questions or scenarios you’d like us to cover, let us know.

Disclaimer:​

This analysis is for educational purposes only and is not financial advice. The strategies discussed, particularly those involving shorting options, carry significant risks, especially in volatile markets like cryptocurrencies. This blog does not cover the impact of margin, which can increase risk for traders.

What is Realized Volatility?​

Realized Volatility (RV) measures the historical volatility of an asset by calculating the standard deviation of its spot price over a defined period. This gives traders insight into how much an asset’s price has fluctuated in the past. For more details on how RV is calculated, refer to here.

The key parameters in RV calculation are the frequency of observations and the lookback period. For instance, daily RV uses daily spot price observations, while weekly RV uses weekly observations. The lookback period determines how far back the analysis goes, providing an average volatility over that time frame. A well-chosen lookback period smooths out short-term fluctuations but remains relevant to current market conditions. If the period is too long, older data may skew the results and fail to reflect the latest market dynamics. Therefore, the lookback period must be long enough to ensure accuracy but not too long to lose relevance.

The graphic above shows the daily Realized Volatility (RV) using different lookback periods (15, 30, 60, and 90 days). As the lookback period increases, RV becomes smoother, reducing the influence of short-term fluctuations. This highlights the importance of selecting an appropriate lookback period when analyzing volatility—it's a crucial parameter for traders.

In this analysis, we focus on daily RV, as our strategy centers around daily expiring options. By aligning the RV calculation with the options' expiration timeframe, we ensure that the volatility we're analyzing is relevant to the short-term nature of the trades.

What is Implied Volatility?​

Implied Volatility (IV) reflects the market's expectations for future volatility. In the options market, IV represents the volatility implied by the market prices of options contracts. For this analysis, we will focus on the 1-day At-The-Money (ATM) IV, which estimates how volatile the market expects the asset to be over the next 24 hours.

The graphic above shows 1-day ATM implied volatility (IV) observed at 8 AM UTC daily, from July 2023 to October 2024. The IV is highly volatile, with significant fluctuations occurring from one day to the next. For example, on August 3rd, 5th, and 6th, 2024 (highlighted by coloured circles), IV surged from 35% to over 110%, then fell back to 75% the following day.

These significant changes in implied volatility (IV) are the result of short-term market dynamics. To demonstrate this, we’ve plotted the corresponding volatility smiles for the highlighted dates. Since these smiles are well-calibrated, it confirms that the observed IV fluctuations are directly influenced by shifts in market conditions.

Comparing Realized Volatility to Implied Volatility

When Realized Volatility (RV) is lower than Implied Volatility (IV), it suggests that the market may be overestimating future volatility based on historical data. This can create opportunities for traders to sell volatility through strategies like selling straddles or strangles.

However, since RV depends on the lookback period, it's important to determine which RV to compare against IV. In the graphics below, we plot daily ATM IV against RV for different lookback periods. The correlations between the two are weak, ranging from 15% to 24%, indicating that no single lookback period consistently outperforms the others in capturing this relationship.

The percentage of days when daily Implied Volatility (IV) is lower than daily Realized Volatility (RV) for various lookback periods, spanning from 1st August 2023 to 20th October 2024, varies between 50% and 60%.

Trading Strategy Based on RV and IV

Our strategy takes advantage of the difference between Realized Volatility (RV) and Implied Volatility (IV). We’ll compare RV, using different lookback periods, with the 1-day ATM IV at 8 a.m. UTC. If RV is lower than IV, we will sell a 1-day ATM straddle, aiming to profit from the possible market’s overestimation of future volatility.

Why Sell a Straddle?

A straddle is an options strategy where both a call and a put option are sold at the same strike price, with the expectation that the asset's price will remain close to that level. In this strategy, the straddle is held until maturity, without dynamic hedging. The options are sold when implied volatility (IV) is high, particularly when IV exceeds realized volatility (RV), allowing the seller to collect a higher premium.

The strategy profits if the asset's price remains stable, enabling the seller to retain part of the premium. However, it’s important to note that selling options carries significant risk if there are large price movements away from the strike price, as this can result in substantial losses for the seller.

Backtesting the Strategy

We will backtest this strategy and compare it to a simpler approach where we sell the 1-day ATM straddle every day, without considering the relationship between RV and IV. This comparison will allow us to assess how using RV as a signal in our strategy impacts overall performance. Since none of the lookback periods showed a clear advantage in the earlier analysis, this parameter will need to be calibrated during the backtest. It is a crucial element of the strategy that requires optimization.

For this analysis, we will use the average mid 1d-ATM volatility observed in the market. The straddle will be sold at the bid price, reflecting the highest price buyers are willing to pay. We will apply a 5% volatility spread as a proxy, which is a conservative estimate within the typical bid-ask volatility spread range of 3-8%, accounting for the difference between buying and selling volatility. This adjustment ensures that the strategy factors in market liquidity and spread costs.

Additionally, trading commissions will be included, similar to the fees charged by major exchanges. A fee will be applied for opening positions, calculated as a percentage of the spot index price of the underlying asset (typically 0.03%) at the time of the transaction, multiplied by the number of contracts. These fees will be capped in line with industry-standard fee structures as a percentage of the option price.

Conclusion

The backtesting results demonstrate that the strategy is sensitive to the chosen lookback period, with the 90-day lookback providing the best PnL profile while reducing the number of trades. These findings underscore the value of using Realized Volatility (RV) as a filter in options trading strategies. Incorporating RV as a volatility indicator can enhance the base strategy of selling daily 1D ATM straddles by mitigating risk during periods of high volatility and optimising overall performance.

By combining historical volatility measures, such as RV, with options trading strategies, traders can gain deeper insights and make more informed decisions. This approach highlights the potential to improve traditional options strategies by integrating reliable volatility metrics into the trading process.

Disclaimer:​

This article is purely instructional and is not financial advice. Long options trading comes with strategic advantages and risks, including the potential loss of the entire premium paid. While long options avoid the liquidation risks associated with futures, if the option expires out of the money, the premium is lost. Additionally, shorting options carries significant risks and is not discussed in this article.

The Dangers of Leverage Trading with Futures​

Let’s use Deribit as an example. On this platform, the initial margin for futures leverage trading starts at 4%, allowing traders to leverage up to 25x their capital. While margin requirements increase slightly with position size, we’ll ignore that for simplicity.

Imagine you open a BTC futures position at $56,000 with 25x leverage. The initial margin required would be:

So, you need $2,240 to control a $56,000 position. Now, if the price rises to $64,000 (a market increase of 14.2%), your profit would be:

This results in a net profit of:

This example demonstrates the appeal of leverage trading—large returns with relatively small initial capital.

However, the maintenance margin for the same futures contract is typically 2%. This means that if the BTC price drops by just 2%, your position could be liquidated, resulting in a 50% loss on your initial investment. In the highly volatile crypto markets, a 2% price swing can occur within minutes, making leverage trading particularly risky. To mitigate this risk, it's crucial to set stop-losses or implement other risk management strategies.

The Power of Options in Leverage Trading​

Now, let’s explore options—a more flexible and controlled way to leverage trades. While traditionally used for risk management, options also serve as powerful tools for speculation, offering both better control over downside risk and the potential for upside gains.

On platforms like Deribit , going long on an option means the only capital at risk is the premium you pay upfront. Unlike futures, there are no margin requirements, so liquidation is not a concern, even if the market moves against you. This provides traders with greater peace of mind while still offering the opportunity for significant returns.

For example, let’s say you purchase a 6-month call option with a $60,000 strike price while the spot price is $56,000. This option gives you the right (but not the obligation) to buy BTC at $60,000 upon expiration. However, you don’t have to wait until maturity to benefit—you can sell the option at any time. If the market moves in your favor, meaning the BTC price increases, you can lock in profits without needing to wait to exercise the option.

The option premium is influenced by factors such as implied volatility $(\sigma)$, time to maturity $(T)$, and the underlying asset price $(F)$. A simplified formula to estimate the premium for an at-the-money (ATM) call option is:

This formula gives a quick approximation of the option premium, highlighting the importance of volatility, time, and asset price in determining the cost of the option. For instance, with an implied volatility of 50% and a 6-month maturity, the premium for an ATM call option on BTCUSD might be:

This premium is much cheaper than buying the underlying asset outright. Additionally, purchasing an out-of-the-money (OTM) option (e.g., a Call option with a strike price of $60,000 when BTC is at $56,000) offers an even cheaper premium while still providing leveraged exposure to price movements.

Options provide leverage through their premium structure. For at-the-money (ATM) options, the leverage factor is inversely proportional to $\sigma\sqrt{T}$. This means lower volatility $(\sigma)$ and shorter time to expiration $(T)$ offer higher leverage. This principle applies broadly to all options—lower volatility and shorter time horizons generally provide higher leverage, but they also come with increased risk due to the shorter time window for the trade to move in your favour.

If the option remains out-of-the-money (OTM) by expiration, the buyer loses the entire premium. However, if the option goes in-the-money (ITM) (for example, if the spot price rises above the strike price for a call), the option holder can make substantial profits. Importantly, the trader does not need to wait until expiration and can unwind the position at any time, locking in profits before maturity if the market moves favourably.

Scenario Comparison: $50$ vs. $70$ Implied Volatility​

Below are two tables comparing different scenarios at 50% and 70% implied volatilities. The option buyer purchases a call option with a strike price of $60,000 when the spot price is $56,000, with maturities ranging from 2 days to 1 year. The tables illustrate how the option's value changes if the spot price drops by 2% to $54,800 (where a leveraged future would suffer a 50% loss due to liquidation) or rises by 14% to $64,000 within a 1-hour timeframe for simplicity of the example.

Key Takeaways​

As shown in the tables, higher volatility provides lower leverage but also reduces the losses. The potential gains for short-tenor options like 2-day options are significant but come with high risk, as the likelihood of hitting the target price within such a short time is low.

Longer maturity options, on the other hand, allow more time for the market to move in your favour, offering a safer approach. The user can give the option time to recover losses and see the trade hypothesis play out.

With options, the trader is not worried about liquidation and retains full control over the strategy. Choosing the right maturity, strike, and understanding volatility levels provides flexibility in managing risks and rewards. A good strategy is one where the hypothesis is satisfied fairly quickly and allows the trader to exit with high gains without sticking too long in the option position and seeing the value eroding due to time decay.

An example of strategy and performance​

Since March 2024, BTC has been ranging between $50K and $70K. In this signal generation, we use simple technical analysis to detect a possible trend for leverage trading using options. Let’s use Heikin Ashi on daily candles. Heikin Ashi is a type of candlestick chart that smooths out price data and highlights market trends by averaging price movements. Unlike traditional candlesticks, Heikin Ashi reduces noise in volatile markets, making it easier to identify trends and potential reversals.

A basic strategy is to go long once the daily chart switches from red candles to green candles, following the close of the first green candle.

Visually, this strategy would have produced several winning trades and only a few minor losses. To increase the likelihood of winning, we add a powerful indicator: the Relative Strength Index (RSI). We go long only when a bullish reversal is detected. Using TradingView and our data, we observe the closure of a first green candle on 10th September 2024, following a series of red candles, alongside a bullish RSI reversal (i.e., lower lows on the price with higher lows on the RSI). The combination of these two events suggests a probable new positive trend, with an estimated likelihood of over 50%.

This is a simple example for illustrating option leverage. Traders can apply their own rules to detect trends or market moves.

On 10th September 2024, BTC’s price at candle close was around $56K, consistent with our earlier analysis. Based on this, we decided to go long with two out-of-the-money options: one with a short expiration of 18th October 2024 and another with a longer expiration of 25th June 2025. Both options, available on Deribit, have a strike price of $60K.

The results are shown below.

Looking at the long-dated option, where market volatility (orange curve) is around 64%, as BTC rises from $56K to $64K between the 10th and 24th September, the option generates a net profit of 42%, offering a leverage factor close to 3 (42% profit compared to BTC's 14% price increase).

On the other hand, the short-dated option delivers an impressive 185% profit, translating to a leverage factor of 13 relative to BTC's price movement. These results align well with the approximation tables provided earlier, highlighting the potential for significant gains with shorter-tenor options.

Conclusion​

In summary, while futures offer substantial leverage, they come with constant risk of liquidation. Going long options, on the other hand, provide more complex leverages with several degrees of freedom and offer a great variety of strategies with no risk of liquidation, making them a smarter choice for traders who want to maintain flexibility and control over their capital.

Long options still carry significant market risk, and the total loss of the premium paid can occur; therefore, a proper understanding of the risks involved is crucial.

In volatile markets like crypto, options give traders the time and tools to manage risk better while still benefiting from price movements.

This chart shows Bitcoin's (BTC) realized volatility over the past year. The x-axis represents time, while the y-axis shows the annualized realized volatility percentage. Higher realized volatility zones indicate periods of increased market activity and price changes.

What is Realized Volatility?​

Realized volatility is calculated based on historical price data and is mathematically defined as the standard deviation of past returns. It measures the historical price fluctuations of an asset, providing an indication of its actual volatility. Typically expressed as an annualized percentage, realized volatility offers a standardized method for comparing the volatility of different assets over various time periods.

There are multiple methods to calculate realized volatility. These parameters can be chosen by the user to adjust according to their needs.

Calculating Realized Volatility​

where:

• $N$ is the number of observations (days),
• $r_i$ is the daily return,
• $\bar{r}$ is the average daily return,
• $A$ is the annualization factor and corresponds to the number of trading days in a year. For digital assets, since they are traded continuously, it is natural to take this number equal to $365$.

Realized Volatility vs. Implied Volatility​

Volatility is crucial for option traders as it affects option prices; higher volatility generally makes options more valuable. While realized volatility measures historical price movements, implied volatility represents the market's expectations of future volatility.

• Implied Volatility (IV): Derived from the prices of options, IV reflects the market's forecast of future price fluctuations. It is forward-looking and can change rapidly based on market conditions.

• Realized Volatility (RV): Based on historical data, RV measures past price fluctuations over a specific period, providing a backward-looking perspective.

The two quantities are often highly correlated. Implied volatility corresponds to the market's expectation and the price of the option, while realized volatility reflects the actual volatility observed in the underlying market.

A historical analysis of IV versus RV can provide traders with insights into periods when options are underpriced or overpriced, thus identifying potential trading opportunities. For example, in the equity market, realized volatility is typically below implied volatility.

A similar analysis for the crypto market, along with the reasons for such behavior, will be covered in another blog.

Importance of Realized Volatility in Digital Asset Markets​

Realized volatility plays a significant role in digital asset markets for several reasons:

• Pricing Derivatives: The options market for major crypto assets such as BTC, ETH, DOGE, and MATIC is well-established. However, there is increasing demand for non-quoted options on smaller digital assets. Given the high correlation between RV and IV, the realized volatility of an asset can serve as a proxy for its implied volatility. Market makers can adjust this measure based on their holdings and their views on future volatility levels and risk premiums.

• Trading strategies: Understanding the historical volatility of an asset and its microstructure in comparison to implied volatility can help traders and market makers develop strategies to exploit market imbalances.

• Market Sentiment: Analyzing volatility trends can provide insights into market sentiment. High volatility periods might indicate market uncertainty or significant news events impacting the asset. This metric, alongside option market data, can help adjust trading strategies.

Realized Volatility in Digital Markets​

Digital asset markets have unique characteristics that affect realized volatility:

• Higher Volatility: Digital assets are generally more volatile compared to traditional assets, resulting in higher realized volatility that reflects more significant price swings.
• 24/7 Trading: Unlike traditional markets, digital asset markets operate 24/7. This continuous trading leads to more pronounced volatility patterns, with potential spikes during traditionally "off-peak" hours.

Advanced Techniques for Measuring Realized Volatility​

While the standard deviation of daily returns is a common method for calculating realized volatility, more advanced techniques can provide deeper insights:

• GARCH Models: Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models estimate volatility by considering past variances and returns. These models are particularly useful for capturing volatility clustering, where periods of high volatility are followed by high volatility, and low volatility periods follow low volatility.
• High-Frequency Data: Using high-frequency data, such as minute-by-minute prices, offers a more granular view of volatility. This approach is especially relevant for digital asset markets, which operate 24/7 and can experience rapid price changes. Users can assess RV with any granular frequency and loop-back period, providing additional microstructure insights.
• Realized Kernels: Realized kernels are advanced statistical tools that account for microstructure noise in high-frequency data. They provide more accurate volatility estimates by filtering out noise and focusing on genuine price movements.

Conclusion

Realized volatility is an important metric for understanding the past behavior of underlying assets. It serves multiple purposes in the digital asset space, such as aiding in the pricing of over-the-counter options or non-listed crypto options. A granular analysis of RV and IV can reveal trading opportunities and improve risk management strategies by providing deeper insights into market sentiments. In a future blog, we will explore this relationship further within the crypto space.

The volatility surface is a financial object that provides the volatility for any given expiry and strike price. This mid-volatility surface is derived from the bid and ask prices quoted in the options market using a smile model, which involves a fitting process and an interpolation across expiries.

Using bid/ask quotes directly to mark a derivatives portfolio is not feasible because different positions might require different volatilities—some should use bid volatility and others ask volatility. For complex derivatives that cannot be easily replicated with vanilla options, it becomes unclear whether to use bid or ask volatility.

Therefore, it is essential to construct a mid-volatility surface. This approach offers a consistent and unique view of the portfolio's value and associated risks.

Introduction to the Volatility Smile​

In financial markets, the volatility smile is a characteristic of the options market where implied volatility varies across different strikes. This behavior contradicts the assumptions of the Black-Scholes model, which presumes constant volatility across strikes. As a result, the Black-Scholes model often leads to pricing inaccuracies, particularly for deep in-the-money and out-of-the-money options.

Why Does the Volatility Smile Occur?​

The volatility smile can be attributed to several market factors:

• Market sentiment and demand: High demand for out-of-the-money puts and calls can increase their prices and thus their implied volatilities.
• Stochastic nature of volatility: Volatility itself can be volatile and mean-reverting.
• Jump risk: Sudden jumps in asset prices, which are not accounted for in normal distributions used in simpler models.

Modeling the Volatility Smile​

To account for the smile, several models have been developed. Here, we focus on two main types: the SABR and SVI models.

SABR Model​

The SABR model is a popular choice for modeling options volatilities in the interest rate and equity derivatives markets. The model is particularly favored for its ability to capture the correct skewness and smile shape of the volatility surface as observed in market data. The model is derived from a stochastic diffusion of the underlying asset of the option.

The dynamics of the SABR model are described by the following stochastic differential equations (SDEs):

Where:

• $S_t$ is the forward price of the asset.
• $W_t$ is brownian motion driving the asset and $B_t$ the driver of the stochastic volatility.
• $Z_t$ is the normalised stochastic volatility factor.

The asset has a CEV (constant elasticity of variance model) like dynamic driven by the $\beta$ parameter. $\beta=1$ gives a log-normal diffusion and $\beta=0$ gives a normal diffusion. $\alpha$ is the CEV volatility.

The stochastic volatility has a log-normal diffusion with a volatility given by $\nu$. The asset and the stochastic volatility are correlated.

Let's provide some intuition on the SABR parameters:

• $\alpha$ controls the at-the-money (ATM) volatility and the overall level of the smile.
• $\rho$ governs the volatility skew, or equivalently, the slope of the smile around the ATM strike.
• $\nu$ determines the convexity of the smile.
• $\beta$ plays a dual role: it influences the relationship between the ATM volatility and the forward price while overlapping with $\rho$ to offer additional flexibility in controlling the skew.

The volatility surface is defined by the popular formula derived in the original SABR paper:

where $S_m=\sqrt{S_0K}$ and $z=\frac{\nu}{\alpha}S_m^{1-\beta}ln(\frac{S_0}{K})$

This formula is an approximation of the implied volatility of the SABR diffusion

QSVI Model​

The SVI model by Gatheral is another popular smile model. Unlike SABR, which is based on a stochastic volatility diffusion, the SVI model is a parametric representation of the option smile.

For a given expiry the volatility smile is given by the formula

where k is the log-moneyness $k=ln(\frac{K}{S_0})$

Gatheral suggests a re-parametrisation of the model which is more intuitive

The new parameters have clear meanings:

• $\sigma_{ATM}$ is the at-the-money (ATM) volatility.
• $\sigma_{min}$ is the minimum volatility on the smile.
• $S_{ATM}$ is the smile slope at the ATM strike.
• $S_L$ is the asymptotic slope of the smile for low strikes.
• $S_R$ is the asymptotic slope of the smile for high strikes.

In our platform, we've developed an advanced extension of the SVI smile model to overcome its limitations and enhance its accuracy. While the SVI model, similar to the SABR model, includes parameters for ATM volatility, skew, and convexity around the ATM strike, it often struggles to fit both low and high strikes accurately due to its wing skew limitations. To address this, we've created a custom extension called the QSVI model. The QSVI model incorporates separate drivers for low and high strikes in addition to the standard parameters, allowing for a more precise fit across the entire range of strikes. This innovation provides traders with more reliable data and improved modeling capabilities, making our platform a superior choice for options and derivatives trading.

Below, we compare the QSVI smile and the SABR smile for the 3-month expiry, both fitted to the same market data. For a range of strikes around the ATM, both models produce similar volatilities. However, noticeable differences emerge on the far left and right wings. This discrepancy arises because there are no quotes for the far out-of-the-money (OTM) or in-the-money (ITM) strikes, and the extrapolation on the wings is driven solely by each model's parameterization. Additionally, SABR has fewer degrees of freedom compared to QSVI for the wings.

Fitting process​

The smile fitting process is a delicate procedure that requires careful attention to the nuances of the options market data. It is essential to understand the specific market data we are trying to fit and adapt it accordingly to align with the smile model.

For options traded on exchanges, such as cryptocurrencies, equity stocks, or commodity assets, the data structure differs significantly from that of over-the-counter (OTC) options like FX options or interest rate options. Typically, exchange-traded options list a set of absolute strikes that change daily to reflect spot market movements. Additionally, the liquidity of option prices across expiries can vary widely and change over time. Some expiries may have only a few quoted strikes, while others may have many. Liquidity drops can cause certain expiries to disappear from the options quotes altogether. The bid/ask spread can also be inconsistent across strikes, leading to potential calendar or butterfly arbitrage opportunities within the smile.

OTC options, on the other hand, are generally simpler in this regard. They are typically quoted on a standard set of strikes across expiries and over time. The mid volatilities for OTC options are marked consistently and rarely imply arbitrage opportunities.

Options bid/ask data​

This section will focus on BTCUSD options traded on exchanges such as Deribit and OKX. These exchanges provide a list of bid and ask prices for call and put options across various expiries and strikes at any given time. Typically, the exchanges quote options with daily, weekly, monthly, and quarterly expiries. Each time one of these expiries matures, the exchange introduces a new one to replace it. For example, there is a 1-day expiry every day and a 1-week expiry every Friday.

The range of quoted strikes is designed to cover a meaningful delta range, with granularity based on the asset's typical daily movement.

Cleaning of bid/ask data​

The bid/ask prices are not always consistent across expiries and strikes, meaning they may not be arbitrage-free. Therefore, we clean the bid/ask price data before fitting it.

Here is a brief description of the steps we take to clean the data:

• Retain only out-of-the-money prices: puts for strikes below the forward price and calls for strikes above the forward price.
• Remove all bid/ask pairs where the bid-ask spread exceeds a certain threshold, typically when the spread divided by the forward price is above 6% (we use this valued based on the analysis of the historical data of the bid-ask spreads).
• Eliminate all call or put prices that are not monotonic in strike.
• Remove all successive call or put prices that imply a digital option price above 1.
• Remove all successive call or put prices that imply a butterfly spread price below 0.

We apply these steps to both the bid and ask prices independently.

After that, we obtain a set of arbitrage-free bid/ask prices. For a given strike, it is possible to have only a bid or only an ask, either because the exchange did not quote both or because the cleaning process removed one of them.

Finally, we calculate the implied volatilities for each bid and ask price and fit the model to this data.

Calibration​

Calibration of the smile model involves adjusting the model parameters to ensure that the model prices align with the observed market prices. This process begins with cleaning the data and computing the implied volatilities from the bid/ask prices. We then fit a unique set of model parameters for each expiry. Since shorter expiries have a narrower range of strikes, and our goal is to maintain stable wings over time, we start by independently fitting expiries with a sufficiently large strike coverage.

To achieve this, we minimize the distance to the mid volatility as well as the bid and ask volatilities, applying a heavier penalty for deviations from the bid/ask prices than from the mid. Additionally, we incorporate a calendar arbitrage penalty to prevent the variance of the current slice from being lower than that of the previous slice.

After fitting these longer expiries, we proceed to fit the shorter expiries. For shorter expiries, we impose an additional constraint on the smile wings, keeping them close to the previous slice's wings. This is necessary because short expiries often lack quotes for low and high strikes, providing insufficient data for the smile model to determine a unique solution. As shown in the first picture below, short expiries typically have bid/ask prices within a narrow range around the ATM, unlike longer expiries. This is because, for short expiries, options with strikes far from ATM have little chance of moving close to ATM by expiry, so the market does not quote strikes far from ATM.

The lack of information on the far wings poses a challenge for fitting the model, as the optimizer can easily become trapped in local minima far from the optimal solution. Therefore, we anchor the short expiry wings to the long expiry wings, which have more quotes on the far wings.

Below, we show three expiries: 5Apr24, 28Jun24, and 27Sep24. For the longer expiries, the bid-ask spreads are wider and more noisy, which can sometimes induce arbitrages. These arbitrages are addressed through the data cleaning process described above.

Options on digital assets are financial derivatives that provide the holder the right, but not the obligation, to buy or sell a digital asset at a predetermined price within a specified timeframe. These options work similarly to traditional options found in equity and foreign exchange (FX) markets, but they are tailored to the unique characteristics of digital assets such as Bitcoin (BTC), Ethereum (ETH), and other cryptocurrencies.

What is an Option?​

An option is a contract that gives the buyer the right to buy (call option) or sell (put option) an asset at a specific price (strike price) on or before a certain date (expiration date). The buyer pays a premium for this right, which is the price of the option. If the option is not exercised by the expiration date, it expires worthless, and the buyer loses the premium paid.

Peculiarities of Digital Asset Markets​

Digital asset markets differ from traditional equity or FX markets in several key ways:

• Volatility: Digital assets are generally more volatile than traditional currencies. This higher volatility can lead to larger price swings and higher potential returns, but also increased risk. For instance the implied volatility, close to the money, can sometimes be 10 to 15 times higher on digital assets markets than FX traditional currency pairs.

• Market Structure: Digital asset markets operate 24/7, unlike traditional FX or equity markets which have defined trading hours. This constant trading can lead to more continuous price discovery but also to potential issues with liquidity during off-peak hours.

• Regulation: The regulatory environment for digital assets is still evolving and varies significantly across different jurisdictions. This can impact the availability, pricing, and trading of options on digital assets.

• Settlement: Unlike traditional equity options that settle in fiat currencies, options on digital assets may settle in either the digital asset itself (e.g., BTC) or in fiat currency (e.g., USD). This is similar to what is seen on FX markets. In fact, a significant number of options are settled in Bitcoin. This means that upon expiration, the option is settled by transferring BTC rather than fiat currency. However, there are also options that settle in USD, or pegged assets such as USDT and USDC, especially on platforms that cater to more traditional investors. In the digital asset space, this is sometimes refereed to as "inverse" vs "linear" options. From a foreign exchange perspective, the settlement is generally referred to as foreign or domestic currency settlement and both can be equally frequent depending on the trading perspective and market conventions. The settlement method chosen can impact the liquidity and pricing of the options.

Options on Future​

In the digital asset options market, particularly for Bitcoin, the options are often written on futures contracts rather than directly on the BTCUSD spot price. These futures contracts themselves are tied to an index, which can aggregate the prices from multiple exchanges to create a representative value of Bitcoin. This index is not actively traded; instead, the futures contracts based on this index are what get traded. Very often, the options on these futures inherit the expiration dates and other characteristics of the underlying futures contracts. This structure introduces a slight layer of complexity, as the performance of the options is indirectly linked to the BTCUSD spot price through the intermediate step of the futures contracts and the index they are based on.

However, because most futures and options on digital assets are designed to have matching expiry dates, the fact that options are written on futures rather than directly on the spot price does not have an impact. At the expiry date, the price of the futures contract converges with the price of the underlying index. This means that for practical purposes, the value of the options at expiry will reflect the intrinsic value of the option on the underlying index.

This differs from e.g. commodity markets where underlying future contracts can have very different expiry dates as the options.

It is worth noting that, on platforms like Deribit, the settlement price of options is determined by averaging the underlying index price over a 30-minute period before expiry, reducing susceptibility to market manipulation and ensuring a fair settlement.

Cash Settlement​

As a general rule, most options on digital assets are cash-settled. This means they pay out the "cash value" in a specified asset, typically either Bitcoin (BTC) or US Dollars (USD) for the BTCUSD pair. Cash-settled options simplify the settlement process by eliminating the need to exchange the actual underlying asset. For BTCUSD options, this could mean receiving the equivalent value in USD or BTC upon expiration.

Physically settled options, which would involve generating two cash flows in both directions (one in BTC and one in USD), are less standard in the digital asset markets. In this type of settlement, the holder would receive the underlying BTC and simultaneously pay the strike price in USD, or vice versa. While physically settled options offer a more direct exposure to the underlying asset, they are more complex to manage due to the need to handle the actual transfer of assets.

The preference for cash settlement does not significantly impact the market value of these options as long as payment conventions and settlement dates remain consistent. The critical aspect is that the settlement mechanism is well understood and accepted by market participants.

Payoff Profile​

We plot below the payoff profile for a BTCUSD option settled in USD and a notional of 0.1 BTC, assuming a premium of 1,000 USD.

And we plot below the payoff profile for a BTCUSD option settled in BTC and a notional of 0.1 BTC, assuming a premium of 0.01 BTC.

One can see that the two types of vanilla options conventions, i.e. "linear" or "inverse", as sometimes referred to in digital assets exchanges, display a different payout profile depending on the payment asset. However, it is important to bear in mind that these payoffs are not seen from the same risk perspective, or the same risky 'unit'. If we were to convert all the cash flows into a single asset, both payout would match by arbitrage reasoning. In other words, assuming no interest rates or cross-currency basis, the market values of each convention are linked by today's spot price. This is a very common setup in FX markets where both foreign and domestic currencies can be risky assets depending on the trader's perspective or location.

Market Risk and Delta Hedging

Delta is a key concept in options trading, representing the sensitivity of an option's price to changes in the price of the underlying asset. Delta hedging is a strategy used to mitigate risk by maintaining a delta-neutral position, where the portfolio's overall delta is adjusted to zero. This involves buying or selling the underlying asset in proportions that offset the delta of the options held, thus protecting against price movements and allowing for more stable returns.

While premiums need to agree irrespective of the "unit" currency chosen, delta used to hedge against the underlying price moves will depend on what is the risky asset from the investors' perspective. For instance, if an investor considers BTC as a risky asset with respect to USD, which is generally the case, then a premium paid in BTC also can be considered risky and can be used to partially hedge the risk of the option itself. This is very similar to FX markets and accurate delta calculations with accurate conventions becomes required.

Below is represented the delta from the Qytrees Dashboard for premiums traded in BTC when the investor considers USD his/her non-risky asset, which gives rise to a shape different from the usual Black--Scholes delta:

The x-axis is the moneyness, that is $K / F(0, T)$ in % where $F$ is the forward price of the respective expiry date $T$. The y-axis represents the premium-adjusted delta where we can notice the impact of the adjustment compared to a classical delta which would grow close to one for small strikes. This delta for instance, would differ from the simplified example discussed above, which showcases the importance of accurate conventions.

Conclusion

In conclusion, the options market for digital assets like Bitcoin and Ethereum shares similarities with traditional markets but also possesses unique characteristics tailored to the volatility, market structure, and regulatory environment of digital assets. The practice of writing options on futures contracts tied to an index, as seen on platforms like Deribit, introduces a small layer of complexity but also ensures stability through mechanisms such as price averaging for settlement. Cash settlement remains the prevalent method, simplifying the process by eliminating the need to exchange the underlying asset. Finally, understanding the payoff profiles and the significance of delta hedging is crucial for managing market risk effectively.

In the second part of this blog post, we will discuss the mathematical details and explain specifically how we implemented this on the Qytrees platform.