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.

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.

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.

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:

$$\text{Initial Margin} = 4\% \times 56,000 = 2,240 \, \text{USD}$$

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:

$$64,000 - 56,000 = 8,000 \, \text{USD}$$

This results in a net profit of:

$$\frac{8,000 - 2,240}{2,240} = 257\%$$

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:

$$\text{Premium} \approx 0.4 \sigma F \sqrt{T}$$

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:

$$\text{Premium} \approx 0.4 \times 0.5 \times 56,000 \times \sqrt{0.5} = 7,919 \, \text{USD}$$

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.

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.

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.

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