In this post, we discuss how implied volatility (IV) is compared across different strikes, maturities. We’ll show how moneyness, log-moneyness, and delta quoting conventions help you visualize and interpret the “volatility smile.” Finally, we’ll highlight how an adaptable API—like Qytrees—streamlines retrieving and analyzing these data points.

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.

In this blog, we discuss the relationship between realized volatility (RV) and implied volatility (IV), focusing on BTC as a case study. The goal is to introduce a simple option trading strategy that takes advantage of potential mispricing between RV and IV. We'll then compare the performance of this strategy against an alternative approach that doesn't incorporate RV information, highlighting the value of using RV in volatility-based trading strategies.

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.

Leverage trading is a popular strategy among traders seeking amplified returns, especially in the volatile crypto markets. However, with high rewards come significant risks. Liquidations are common in futures trading, often resulting in substantial losses. For instance, on August 5, 2024, a significant market decline led to the liquidation of nearly 300,000 crypto traders from their leveraged positions or collateral trades, according to data from Coinglass. Reference

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.

Realized volatility is a statistical measure that quantifies the degree of variation in the price of a financial asset over a specific period. This metric provides insights into the past behavior of asset prices and can be valuable for derivative traders.

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.

A trader or investor holding a portfolio of options or other derivatives based on a given underlying asset —be it cryptocurrency, an index, or a stock— needs a mid-volatility surface to accurately mark the portfolio to market at any point in time.

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.

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.