Absolute volatility smile: Meaning, Criticisms & Real-World Uses

What Is Absolute Volatility Smile?

The absolute volatility smile is a graphical representation within the realm of financial derivatives, specifically concerning options pricing models. It illustrates the relationship between the strike price of an option and its implied volatility for a given expiration date. When implied volatility is plotted against strike price, the resulting curve often exhibits a distinctive U-shape, resembling a "smile." This pattern signifies that options that are significantly in-the-money (ITM) or out-of-the-money (OTM) tend to have higher implied volatilities than those at-the-money (ATM). The presence of an absolute volatility smile challenges the fundamental assumptions of earlier models, such as the Black-Scholes model, which posits a constant implied volatility across all strike prices for a given maturity.

History and Origin

Prior to the momentous market events of October 1987, standard option pricing models, including the then-dominant Black-Scholes model, assumed that the implied volatility of an underlying asset remained constant regardless of the option's strike price. This assumption would lead to a flat line when plotting implied volatility against strike price. However, the severe market downturn known as Black Monday in October 1987 profoundly reshaped market perceptions of risk, particularly the likelihood of extreme price movements. Post-1987, empirical observations revealed that options far from the money (both ITM and OTM) were trading at prices implying higher volatilities than ATM options. This phenomenon, which visually formed the characteristic "smile" shape, was first notably observed in equity options markets following the 1987 stock market crash.¹², ¹³ This discrepancy highlighted that market participants were willing to pay a premium for protection against or participation in large, infrequent price swings, leading to the emergence and widespread recognition of the absolute volatility smile.

Key Takeaways

The absolute volatility smile graphically depicts how implied volatility varies with the strike price for options sharing the same expiration date.
It typically shows higher implied volatilities for deeply in-the-money and out-of-the-money call options and put options compared to at-the-money options.
The smile contradicts the assumption of constant volatility in the Black-Scholes model, reflecting real-world market perceptions of tail risk.
Understanding the absolute volatility smile is crucial for accurate option valuation, risk management, and developing sophisticated options trading strategies.

Interpreting the Absolute Volatility Smile

Interpreting the absolute volatility smile offers valuable insights into market sentiment and expectations regarding future price movements of the underlying asset. The "smile" shape indicates that market participants assign a higher probability to extreme price changes (both significant increases and decreases) than what would be predicted by a log-normal distribution, which is a key assumption of some traditional option pricing models.

A pronounced smile often suggests heightened market uncertainty or a belief that large price swings are more likely. The higher implied volatilities at the "wings" (far from the at-the-money (ATM) strike) imply a higher perceived risk of the underlying asset moving substantially in either direction by the expiration date. Conversely, a flatter smile indicates that market expectations for extreme movements are lower. Traders can analyze the slope and curvature of the absolute volatility smile to gauge whether the market is pricing in more downside risk (a steeper left wing for puts) or upside potential (a steeper right wing for calls), or an equal probability of large moves in either direction.

Hypothetical Example

Consider a hypothetical stock, XYZ Corp., currently trading at $100. An investor is observing the implied volatilities for XYZ options with an expiration date three months from now:

Strike Price $90 (OTM Put / ITM Call): Implied Volatility = 28%
Strike Price $95 (OTM Put / ITM Call): Implied Volatility = 25%
Strike Price $100 (ATM): Implied Volatility = 22%
Strike Price $105 (ITM Put / OTM Call): Implied Volatility = 25%
Strike Price $110 (ITM Put / OTM Call): Implied Volatility = 28%

If these implied volatilities are plotted on a graph with strike price on the x-axis and implied volatility on the y-axis, the resulting curve would clearly show the U-shaped absolute volatility smile. The lowest implied volatility (22%) is observed at the at-the-money (ATM) strike of $100, while it increases as the strike price moves further away from $100 in either direction, demonstrating the characteristic smile pattern. This suggests that the market anticipates a higher probability of significant price movements for XYZ Corp. (either below $90 or above $110) than a simple constant volatility model would predict.

Practical Applications

The absolute volatility smile has several important practical applications in financial markets, particularly within options trading and risk management.

Option Pricing and Valuation: The smile is crucial for accurately pricing call options and put options across different strike prices. By using the implied volatility specific to each strike rather than a single, constant volatility, market participants can derive more realistic theoretical values for options, especially those deep in-the-money (ITM) or out-of-the-money (OTM). This allows traders to identify potentially mispriced options more effectively.¹¹
Risk Management and Hedging: Traders utilize the absolute volatility smile to better assess and manage the risks associated with their options portfolios. For example, if the smile indicates higher implied volatilities for out-of-the-money options, it signals increased market concern about tail risks. This insight can inform hedging strategies, leading traders to potentially adjust their positions or implement more aggressive hedges to protect against large, unexpected price swings.⁹, ¹⁰
Volatility Trading and Arbitrage: The absolute volatility smile can reveal discrepancies in how volatility is priced across different strikes. Sophisticated traders may seek to exploit these differences through arbitrage strategies, such as volatility arbitrage, where they aim to profit from perceived mispricings in implied volatility relative to expected future (realized) volatility.⁷, ⁸

Limitations and Criticisms

While the absolute volatility smile provides a more realistic representation of market expectations than models assuming constant volatility, it is not without its limitations and criticisms.

One primary critique stems from the fact that models like the Black-Scholes model were originally developed under the assumption of constant volatility. The very existence of a volatility smile demonstrates that this assumption does not hold true in real markets, where implied volatility varies significantly with strike price and expiration date. This divergence means that the Black-Scholes model, when used in its basic form, can significantly misprice deep in-the-money (ITM) and out-of-the-money (OTM) options.⁶

Furthermore, while the smile helps to account for "fat tails" (the increased probability of extreme events) in actual price distributions, it is a static snapshot for a given expiration. It doesn't inherently predict how the implied volatility curve itself will change over time or in response to new market information. More advanced models, such as stochastic volatility models, have been developed to capture the dynamic evolution of the volatility surface, acknowledging that volatility itself is not constant but rather a stochastic process.⁵ However, these more complex models can be computationally intensive and challenging to calibrate effectively.⁴ The absolute volatility smile is also influenced by supply and demand dynamics, which can distort its shape from what might be implied purely by underlying risk perceptions.³

Absolute Volatility Smile vs. Volatility Skew

The terms absolute volatility smile and volatility skew are both related to patterns observed when plotting implied volatility against strike price, but they describe different shapes and underlying market sentiments.

The absolute volatility smile is characterized by a symmetrical U-shape, where implied volatilities are higher for both deep in-the-money (ITM) and out-of-the-money (OTM) options, with the lowest implied volatility typically found at the at-the-money (ATM) strike. This pattern suggests that the market anticipates large price movements in either direction (up or down) with increased probability, reflecting a general uncertainty or a perceived higher likelihood of extreme events.

In contrast, a volatility skew (sometimes referred to as a "smirk") represents an asymmetric or slanted curve. While the smile is generally symmetrical, a skew indicates a directional bias in market expectations. For example, in equity markets, a common observation is a "negative skew" or "volatility smirk," where out-of-the-money (OTM) put options have significantly higher implied volatilities than comparable out-of-the-money (OTM) call options or at-the-money (ATM) options. This typically reflects a market preference for downside protection, implying that investors are more concerned about large negative price movements than equally large positive ones. While a smile suggests equal probability for large moves up or down, a skew indicates that one direction is perceived as more likely or more impactful.²

FAQs

Why is the absolute volatility smile important for options traders?

The absolute volatility smile is crucial because it helps options traders understand how the market is pricing in risk for different strike prices and maturities. By recognizing that implied volatility is not constant, traders can make more informed decisions about option valuation, identify potential mispricings, and manage their portfolio risk management strategies more effectively.

Does the absolute volatility smile always appear?

No, the absolute volatility smile does not always appear. While it is a common observation in certain markets, such as near-term equity options and currency options, its shape and prominence can vary.¹ Sometimes, the market exhibits a volatility skew (a lopsided curve) rather than a symmetrical smile, especially in equity index options. The appearance and shape of the smile are influenced by market conditions, supply and demand, and significant market events.

How does the absolute volatility smile relate to the Black-Scholes model?

The absolute volatility smile directly challenges a key assumption of the Black-Scholes model, which is that the implied volatility of an underlying asset remains constant across all strike prices for a given expiration date. In reality, the observed smile pattern shows that implied volatility varies. This means that the basic Black-Scholes model tends to underprice out-of-the-money (OTM) and in-the-money (ITM) options when using a single volatility input derived from at-the-money (ATM) options.

What causes the absolute volatility smile?

Several factors contribute to the absolute volatility smile. One primary reason is the market's perception of "tail risk"—the increased probability of extreme, rare events (like large market crashes or significant rallies) that are not fully captured by the normal distribution assumed in simpler models. Investors are often willing to pay more for put options that protect against large downside moves, and sometimes for call options that capture large upside moves, increasing their implied volatility. Additionally, supply and demand dynamics in the derivatives market can influence the smile's shape.