How to Measure Volatility Skew

To dive into volatility skew, it's essential to understand the concept of implied volatility (IV) first. IV represents the market's expectation of the future volatility of a security's price and is a critical component of options pricing. The Black-Scholes model, for example, uses implied volatility to help estimate fair prices of options contracts.

However, implied volatility is not always symmetrical. When plotted against different strike prices, implied volatility often shows a "skew" or "smile" pattern. This divergence from a flat line is what we refer to as volatility skew. The skew is indicative of market participants' perception of risk at various strike prices. When the IV of out-of-the-money (OTM) puts is higher than that of at-the-money (ATM) or out-of-the-money calls, it's called a put skew, and this can often signal bearish sentiment in the market.

But how do we measure volatility skew? There are multiple methods depending on the context and the trading strategy in play. Below, we’ll walk through some of the most commonly used methods.

1. Skewness Ratio Method

This method involves comparing the implied volatility of options with the same expiration date but different strike prices. One common approach is to take the ratio between the implied volatility of a lower strike put option (which is OTM) and the implied volatility of an at-the-money option. If the ratio is above 1, it indicates the presence of skew.

For example, let’s say we have the following implied volatilities for options expiring in one month:

• ATM Call: 20%
• 90% OTM Put: 25%

The skewness ratio would be calculated as:

A ratio of 1.25 tells us that the market assigns significantly higher implied volatility to the OTM put than to the ATM option, indicating that market participants are pricing in a higher risk for the downside.

2. Implied Volatility Surface

The implied volatility surface is a 3D graph that plots implied volatility against both strike price and time to maturity. The x-axis represents the strike prices, the y-axis shows time to expiration, and the z-axis shows implied volatility. This surface provides a broader view of how implied volatility changes across both moneyness and time, allowing traders to better understand the dynamics of volatility skew.

To measure skew from this surface, traders can observe the curvature at different points, particularly looking for the steepness of the slope between lower strike prices (OTM puts) and higher strike prices (OTM calls). If the surface slopes upwards toward OTM puts, it signals a put skew, while an upward slope toward OTM calls may indicate a call skew.

3. 25-Delta Risk Reversal

The 25-delta risk reversal is a popular metric among institutional traders, especially in the FX and equity markets. This method compares the implied volatility of an OTM call option with a 25-delta to an OTM put option with a 25-delta. In this context, "delta" refers to the sensitivity of an option's price to changes in the price of the underlying asset.

To calculate the risk reversal, subtract the implied volatility of the 25-delta put from that of the 25-delta call. A positive number indicates call skew (higher demand for OTM calls), while a negative number indicates put skew (higher demand for OTM puts).

For example:

• 25-delta Call IV: 18%
• 25-delta Put IV: 23%

The 25-delta risk reversal is calculated as:

In this case, a -5% risk reversal indicates that puts are more expensive than calls, reflecting bearish sentiment in the market.

4. Volatility Smile and Risk Premiums

The volatility smile is another way to measure volatility skew. It refers to the U-shaped curve that forms when plotting implied volatility against strike prices. The smile indicates that options far OTM (either calls or puts) have higher implied volatilities than ATM options. A volatility smile often appears in markets where extreme events (like financial crises) are expected, as traders demand a premium to hedge against such events.

Measuring the steepness and shape of the volatility smile provides a deeper insight into the market's view on tail risk. A steep smile typically indicates a higher premium for tail risk (i.e., the probability of extreme price movements), while a flatter smile may suggest complacency or lower expected volatility.

5. Variance Swap Skew

Variance swaps are another advanced tool used to measure volatility skew. A variance swap allows traders to speculate on the future variance (squared volatility) of an asset's price without having to take directional risk. The skew in a variance swap is measured by comparing the strike price of the variance swap to the implied volatility of ATM options.

If the variance swap price is higher than ATM implied volatility, it may indicate that traders expect higher volatility in the future, especially at the tails. This can be interpreted as a measure of volatility skew, as it signals that the market is pricing in a higher probability of extreme movements.

6. Interpreting Skew for Different Market Conditions

Bullish Markets: In a strong bull market, traders may observe a call skew, where OTM calls have higher implied volatility than OTM puts. This skew suggests that traders are willing to pay more to capture upside potential.

Bearish Markets: Conversely, in a bearish market, a put skew typically emerges. This is due to the increased demand for downside protection, driving up the implied volatility of OTM puts compared to calls. A strong put skew can be a sign of market anxiety or expectations of a downturn.

Neutral Markets: In range-bound or neutral markets, volatility skew might flatten out, with OTM puts and calls having similar implied volatilities. However, even in such markets, slight skews might appear due to sector-specific risks or macroeconomic concerns.

7. Applications of Volatility Skew in Trading

Traders and investors use volatility skew to identify opportunities and manage risk in several ways:

• Hedging Strategies: A pronounced put skew may indicate a good time to buy downside protection. For instance, portfolio managers might buy OTM puts to hedge against potential market declines.

• Arbitrage Opportunities: Savvy traders can exploit differences in skew by constructing option spreads or using volatility arbitrage strategies. A common trade is to sell expensive OTM puts while buying cheaper ATM options.

• Sentiment Analysis: Skew provides insight into market sentiment. A significant put skew often signals fear or pessimism, while a call skew may indicate optimism.

• Tail Risk Hedging: Investors concerned with rare, catastrophic events (often referred to as "black swans") will pay attention to the volatility skew as it can indicate the market's expectation of such events. A steep volatility smile might prompt traders to buy deep OTM puts or calls to hedge against extreme price movements.

Conclusion

Measuring volatility skew is a vital skill for anyone involved in options trading or risk management. Whether through simple methods like the skewness ratio or more advanced techniques like the 25-delta risk reversal or variance swaps, understanding the dynamics of volatility skew can provide critical insights into market sentiment and potential risk. Volatility skew is not just a number—it’s a reflection of how market participants perceive and price in the risks of future price movements. Knowing how to measure it can give traders a significant edge in anticipating and responding to changes in market conditions.