Stock Evolution Under Stochastic Volatility

Abstract

Stochastic volatility appears to be a fact of life in real-world derivatives markets, but it presents huge difficulties for valuation models. Adding a second stochastic variable in addition to the asset price significantly complicates matters. And things become only worse if one wants to model the volatility process realistically, as having a mean-reverting drift of the stock price process as a priced factor. Amercican exercise throws further complications into the situation. A number of useful closed-form and numerical approximation models have been developed over time, but only for particular special cases. In this article, Leisen presents a procedure for constructing a general three-dimensional valuation lattice that can handle a broad range of stochastic volatility models, including those in the literature.