Friday, December 17, 2004

Historical volatility smile

Here's some historical data I dug up. It shows that the actual character of fluctuations in the SP500 changed after the crash of 1987. In particular, the appearance of skew in the implied volatility is reflected in the realized volatility.

For earlier discussion, see here and here.


Anonymous said...


Please explain a bit what I am supposed to find in the appearance of skew in the volatility.


Steve Hsu said...


My interest in the vol skew is a bit esoteric. Basically, it violates the "log-normal random walk" assumption in the Black-Scholes model of option pricing.

In a random walk, the probability distribution for each step is identical and does not depend on how the previous path of the walker.

To someone unfamiliar with the idealized world of financial engineering models, this may sound nutty or naive, since obviously the mood of the market changes due to what has recently happened (a run up, a crash, etc.)

In fact, the data (at least post-1987 crash) does show a very different probability distribution for price fluctations depending on whether the market has been going up or down. This is "skew" in the distribution.

Believe it or not, prior to the 90s or mid-90s this skew was not systematically accounted for in derivatives pricing, although now practitioners are well aware of it.

Anonymous said...

Thanks, thanks.


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