The rapid market collapse that took place between early October and late November 2008 changed options pricing dynamics in two very specific ways:
1. Higher implied volatility across all options contracts
2. Steepened implied volatility skew from low to high strike prices
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These changes create new opportunities that did not exist during the pre-crash era when far out-of-the-money strikes had little to no value for options expiring in the current month. Most of the opportunity is related to the implied volatility skew or “smile” – as it is often referred to. This price distortion is a response to a crashing market where large amounts of money can be lost by investors who sell out-of-the-money puts. The smile first became steep after the 1987 crash that took the market down 25% in a single day. Since then, implied volatility profiles for equity and index options have taken on a distinctly negative skew – that is, volatility tends to rise as the strike price decreases. This effect causes out-of-the-money puts to be relatively more expensive than traditional options pricing theory predicts. Additionally, since put-call parity dictates that the relationship between strike price and implied volatility be the same for both types of contracts, in-the-money calls should also be more expensive. Far out-of-the-money call prices normally flatten out with implied volatility stabilizing several strike prices above the trading price of the stock. This flattening is what gives rise to a curve with a shape that can be referred to as a “smile.”
Goldman Sachs as a Model
Pre- and post crash differences are apparent in the implied volatilities priced into various near-expiration options for Goldman Sachs before and after the market collapse. Table 1 lists implied volatilities for options below and above the stock price on 7/28/2008, 19 days before the August 2008 expiration. Table 2 provides a similar list for the March 2009 expiration (implied volatilities on 3/2/2009, 19 days before expiration).
Table 1: Pre-crash Implied volatilities for Goldman Sachs options prior to the August 2008 expiration. Stock price = $172.90 with 19 days remaining before expiration.
Table 2: Post-crash Implied volatilities for Goldman Sachs options prior to the March 2009 expiration. Stock price = $86.85 with 19 days remaining before expiration.
The differences are striking. Before the large market decline, at-the-money implied volatilities were stable in the 45% range. In the post-crash era, however, implied volatility for at-the-money options was as high as 95%. In percentage terms, the skew between at-the-money and out-of-the-money options was surprisingly flat between the two sets. In the pre-crash era, put volatility grew by 40% from 45% to 63% across six strikes. After the crash, implied volatility grew 43% across six strikes from 95% to 136%. However, in absolute value terms, implied volatility increased much more dramatically after the crash. This distortion creates a much steeper price curve.
The steepness of the second curve is apparent in table 3 which displays prices for the put options listed in table 2 and calculated values for the same options using 1/2 the actual implied volatility.
Table 3: Post-crash Implied volatilities and prices for Goldman Sachs put options prior to the March 2009 expiration (left side of table). Calculated values for the same options with implied volatility reduced by half (right side of table). Stock price = 86.85, 19 days remain before expiration, risk free interest rate = 1.5%.
Implied Volatility #1 (%)
Price #1 ($)
Implied Volatility #2 (%)
Price #2 ($)
The differences become striking when values for out-of-the-money options are compared. With implied volatilities reduced by half, it becomes impractical to structure trades that involve selling $50, $55, $60, $65, or $70 strike prices. These estimates are reasonable because at-the-money options in the pre-crash market traded for slightly less than half their post-crash values ($170 put = 45% implied before the drawdown; $85 put = 95% implied volatility after the drawdown).
Jeff Augen is currently a private investor and writer,and has spent over a decade building a unique intellectual property portfolio of databases, algorithms, and associated software for technical analysis of derivatives prices. This work has been the subject of three books from Pearson Education (Financial Times Press): The Volatility Edge in Options Trading, The Option Trader’s Workbook, and Trading Options at Expiration.