The Heston Model
In 2013 Fabrice Douglas Rouah published The Heston Model and its Extensions in Matlab and C#. Now, for those who feel more at home with Excel spreadsheets, comes The Heston Model and Its Extensions in VBA (Wiley, 2015). It is a condensed and readapted version of the original book, although both books follow the same chapter outline. In the author’s words, “it serves as a ‘VBA cookbook’ for the models covered in the original book, rather than a reference guide for the theoretical aspects of the models.” (p. xvii) VBA code snippets, those that are vital to the calculations, are illustrated in the text and are available for download to those who purchase the book.
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.