Chapter 4. Volatility Skew: Smile or Smirk?

In 1986, traders used the Black-Scholes pricing model to compute the theoretical fair value of an options contract. At the time, most traders assumed that the same implied volatility would apply for all options contracts based on a single underlying stock and with the same expiration date. It was also assumed that all options contracts based on a single stock or stock index should trade with the same measure of volatility, and at-the-money calls and puts with the same strike price and expiration date should have the same volatility.

But that was before the crash of October 19, 1987. On a single day, the Dow Jones Industrial Index fell by 508 points, or 22.6 percent. During that month the index lost nearly a third of its value. Since then, prices for stocks and options contracts have shown a strong negative skew. Mathematically speaking, a negative skew means that projected future prices for contracts tend to move down over time regardless of market conditions. Higher implied volatility is also more common for out-of-the-money puts as compared with put contracts at the money or in the money. The result has come, over time, to be referred to as the risk premium.

Academics who write books and earn PhDs offer explanations for the phenomenon of the negative skew. The implied volatility for put contracts is higher than it "should be" because market liquidity is driven by demand shocks or short supply, because banks and clearinghouses are unwilling ...

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