Wednesday, June 10, 2015
Rouah, The Heston Model
The Heston stochastic volatility model for pricing options was introduced in 1993, six years after the stock market crash of October 1987. The crash, with its subsequent “exacerbation of smiles and skews in the implied volatility surface,” called into question the restrictive assumptions of the Black-Scholes model. “The most tenuous of these assumptions is that of continuously compounded stock returns being normally distributed with constant volatility.” Returns are not normally distributed but exhibit skewness and kurtosis, and volatility is not constant in time but tends to be inversely related to price.
Readers of Rouah’s book should be well schooled in advanced calculus. This is a book for quants, not the casual options trader. As far as I know, no retail options trading platform offers the alternative of using the Heston pricing model even though the deficiencies of Black-Scholes are well documented. In fact, one rationale for sticking with Black-Scholes is precisely that its deficiencies are so well known. The Heston model remains a work in progress.