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Black Monday 1987

The Options Market and Volatility Smiles

Pomegra Learn

Why Did the Options Market Change Forever After Black Monday?

Before October 19, 1987, options traders in equity markets largely priced options according to the Black-Scholes model — a framework that assumed volatility was constant across strike prices and expiration dates. On any given stock, a one-month call option 10 percent out of the money should imply the same volatility as a one-month put option 10 percent out of the money. The mathematics was internally consistent and the model was intellectually elegant. Then Black Monday demonstrated that this assumption was catastrophically wrong — that the probability of a 20 percent decline in a single day was not negligibly small, as the model implied, but was a real possibility that should be priced into deep out-of-the-money put options. The "volatility smile" — the pattern of options pricing that replaced constant volatility — emerged from the wreckage of the crash and has been a permanent feature of equity options markets ever since.

Volatility smile: The empirical pattern in equity options markets, observed universally since 1987, in which implied volatility is higher for out-of-the-money put options (low strike prices) than for at-the-money options, reflecting the market's pricing of crash risk that the standard Black-Scholes model does not incorporate.

Key Takeaways​

  • Before 1987, Black-Scholes implied volatilities were roughly constant across strike prices for equity index options — consistent with the model's assumption of lognormal price processes with constant volatility.
  • Black Monday demonstrated empirically that stock prices could fall 20 percent in one day — an event that the constant-volatility Black-Scholes framework assigned essentially zero probability.
  • After the crash, market makers began systematically pricing out-of-the-money puts at higher implied volatilities than at-the-money options — reflecting the market's demand for crash protection and the recognition that crash risk was severely mispriced.
  • This pattern — called the "volatility smile" or "volatility skew" — has been a permanent feature of equity options markets since 1987 and is absent in markets that have not experienced comparable crashes (some fixed income and currency options still show flatter volatility surfaces).
  • The volatility smile represents an important insight: the distribution of equity returns has "fat tails" — extreme negative outcomes occur more frequently than the lognormal distribution assumes.
  • The VIX — the CBOE Volatility Index — was introduced in 1993 and reflects the options market's aggregate assessment of future volatility, including the crash risk now embedded in put option prices.
  • Options pricing models were subsequently extended (jump-diffusion models, stochastic volatility models, local volatility models) to accommodate the empirically observed volatility surface.

The Black-Scholes World Before 1987​

The Black-Scholes options pricing model, published by Fischer Black and Myron Scholes in 1973 and independently by Robert Merton in the same year, was one of the most influential contributions to finance of the twentieth century. Scholes and Merton received the Nobel Memorial Prize in Economics in 1997 (Black had died in 1995 and was not eligible).

The model derives the fair price of a European option — the right to buy or sell an asset at a specified price on a specified date — under several key assumptions:

  1. The underlying asset's price follows a geometric Brownian motion with constant volatility.
  2. There are no transaction costs and trading is continuous.
  3. There are no dividends during the option's life (or dividends are known and deterministic).
  4. The risk-free interest rate is constant and known.

The critical assumption for the volatility smile story is the first: constant volatility. Under this assumption, a stock with 20 percent annual volatility has the same 20 percent volatility whether it is well above or well below its current price. The probability of any given percentage decline over any given period is fixed and determined by the lognormal distribution.

Before October 1987, equity options markets broadly priced in a manner consistent with this assumption. Implied volatilities — the volatility inputs that made the Black-Scholes model price the observed market price of an option — were roughly similar across different strike prices for the same expiration date. Traders who observed modest differences in implied volatility across strikes generally treated them as noise or as reflecting minor model specification issues rather than as signals of systematic mispricing.

What the Crash Revealed​

October 19, 1987 was a data point. A single-day decline of 22.6 percent in the Dow Jones Industrial Average.

Under a standard Black-Scholes model with 20 percent annual volatility (a reasonable assumption for US large-cap stocks before the crash), the probability of a 22.6 percent decline in a single day is astronomically small — essentially zero for any practical purpose. A daily standard deviation of 20%/sqrt(252) ≈ 1.26% implies that a 22.6% daily move is roughly 18 standard deviations. The probability of an 18-sigma event under a normal distribution is a number so small that it would not occur once in the life of the universe.

Yet it had happened. On a day like any other, with markets opening normally, the primary US equity index had fallen 22.6 percent. The statistical model was not wrong in an ordinary sense — it was not that volatility had been slightly underestimated. It was that the entire probability distribution assumed by the model failed to assign meaningful probability to events that turned out to be possible.

The implication for options pricing was stark: deep out-of-the-money put options on equity indices — options that would pay off in the event of a large, rapid decline — had been catastrophically underpriced before October 1987. They had been priced as if their payoff scenarios were essentially impossible. They were not impossible.

The Emergence of the Volatility Smile​

When options markets reopened in the weeks and months after Black Monday, options traders began pricing out-of-the-money put options at higher implied volatilities. This reflected both the demand for crash protection — investors who had been hurt by the unhedged decline wanted insurance — and the market's revised assessment of crash risk.

The pattern that emerged — systematically higher implied volatility for lower-strike put options — is called the "volatility smile" or "volatility skew" in equity markets. Plotting implied volatility against strike price (for a given expiration), the curve typically slopes downward from left to right: out-of-the-money puts (low strikes) trade at high implied volatility; at-the-money options trade at moderate implied volatility; out-of-the-money calls (high strikes) trade at lower implied volatility.

In equity markets, the smile is asymmetric — it looks more like a smirk, tilted toward the left (put side). This reflects the asymmetric nature of equity crash risk: markets can fall sharply in a way that markets rarely rise sharply. The demand for downside protection exceeds the demand for upside participation (since equity ownership itself provides upside participation).

Fat Tails and the Return Distribution​

The volatility smile is the options market's way of expressing that equity returns have "fat tails" — the probability of extreme events is higher than the normal distribution assumes. In statistical terms, equity returns have excess kurtosis (leptokurtosis): the tails of the distribution are fatter than normal.

Black Monday is the most extreme demonstration, but smaller extreme events are also more frequent than the lognormal distribution predicts. Days with 3 percent or greater moves happen far more often than the lognormal distribution would predict based on typical daily volatility. This property of financial returns was known before 1987 — Benoit Mandelbrot had documented it in the 1960s — but had not been fully incorporated into options pricing practice.

The volatility smile is, in essence, the market's way of pricing fat-tailed distributions without formally abandoning the Black-Scholes framework. Rather than adopting a different distributional model, practitioners maintain the Black-Scholes formula as a "quoting convention" but allow implied volatility to vary with strike price — implicitly using the pattern of implied volatilities to specify a non-lognormal price distribution.

Model Extensions After 1987​

The observed volatility smile motivated a substantial research effort to extend the Black-Scholes model in ways that could generate similar patterns theoretically. The main approaches:

Jump-diffusion models (Merton, 1976; extended post-1987). These add discrete "jump" components to the standard continuous diffusion, allowing for sudden large price moves (crashes) that do not require extreme volatility assumptions for the diffusion component. A model with occasional large jumps naturally produces the observed skew in options prices.

Stochastic volatility models (Heston, Hull-White, Stein-Stein). Rather than assuming constant volatility, these models allow volatility itself to follow a stochastic process. Since periods of high volatility are correlated with market declines (volatility clustering), stochastic volatility models can generate the negative correlation between the underlying return and volatility change that produces the smile.

Local volatility models (Dupire, Derman-Kani, 1994). These models specify volatility as a deterministic function of the current stock price and time, calibrated to match the observed option prices across all strikes and maturities. The Dupire model was particularly influential for derivatives pricing practice.

The VIX and Volatility as an Asset Class​

The Black Monday experience, and the subsequent development of the volatility smile, contributed to the recognition that volatility itself was a quantity that investors might want to trade. In 1993, the Chicago Board Options Exchange introduced the VIX — the Volatility Index — as a measure of the options market's expectation of near-term volatility in the S&P 500.

The original VIX used at-the-money S&P 100 options (OEX); in 2003, it was reformulated to use a wider range of S&P 500 options across multiple strike prices, better capturing the full volatility surface including the skew. The reformulated VIX represents a model-free estimate of expected volatility that incorporates the crash risk premium embedded in out-of-the-money put prices.

The VIX has become one of the most widely watched financial indicators — a "fear gauge" that rises during periods of market stress and falls during periods of calm. VIX futures and options allow investors to take explicit positions on future volatility — something that was not possible before the financial engineering that followed Black Monday created the market infrastructure for volatility trading.

Common Mistakes in Understanding the Volatility Smile​

Treating the smile as a model failure. The volatility smile does not mean Black-Scholes is "wrong" in a way that makes it useless. It remains the standard quoting convention, and the insights about hedging and option combination strategies derived from it remain valid. The smile means that the standard model requires enrichment for accurate pricing across the full surface.

Assuming higher implied volatility means lower value. Options with high implied volatility are not overpriced relative to options with low implied volatility — they simply reflect different market assessments of the relevant risks. Deep out-of-the-money puts have high implied volatility because they provide crash protection that the market prices as valuable, not because they are mispriced.

Frequently Asked Questions​

Why is the volatility smile specific to equity options? The asymmetric crash risk of equities — which can fall sharply and rapidly in a way that equity markets do not typically rise — creates the asymmetric demand for downside protection that drives the skew. Foreign exchange options often show a more symmetric smile, reflecting that currencies can move sharply in either direction. Interest rate options show different patterns reflecting interest rate dynamics.

Is the crash risk premium in put options worth paying for portfolio protection? This is one of the most actively researched questions in options markets. The put protection premium — the amount by which out-of-the-money put implied volatility exceeds realized volatility — has historically been substantial, suggesting that put buyers pay more for protection than its ex-post value warrants on average. However, protection that pays off during tail events (when equity portfolios have declined severely) has value that simple average-return analysis does not capture.

Did Black Monday directly cause the VIX? Black Monday created the demand for a volatility measure and the intellectual framework for thinking about crash risk as a separable dimension of risk. The specific development of the VIX in 1993 reflected both the post-crash research environment and the CBOE's commercial interest in developing new products.

Summary​

Black Monday permanently changed how financial markets price options on equity indices. By demonstrating that crash risk — the probability of extreme negative returns in a single day — was real and had been severely underpriced, the crash motivated the development of the volatility smile: the pattern in which out-of-the-money put options trade at higher implied volatilities than at-the-money options. This smile is not a market inefficiency or a model failure in any simple sense; it is the market's rational pricing of fat-tailed equity return distributions whose crash component was revealed on October 19, 1987. The lasting theoretical legacy was the recognition that continuous-time lognormal models are inadequate for equity markets and that fat tails, jump processes, and stochastic volatility must be incorporated into any framework intended to price derivatives accurately across the full range of market conditions.

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