PT  - JOURNAL ARTICLE
AU  - Natalia A Beliaeva
AU  - Nawalkha Sanjay K.
TI  - A Simple Approach to Pricing American Options Under the Heston Stochastic Volatility Model
AID  - 10.3905/jod.2010.17.4.025
DP  - 2010 May 31
TA  - The Journal of Derivatives
PG  - 25--43
VI  - 17
IP  - 4
4099  - https://pm-research.com/content/17/4/25.short
4100  - https://pm-research.com/content/17/4/25.full
AB  - Lattice models are workhorses of practical option pricing, especially for American options, but an important design criterion is that they need to be set up so that the interior branches recombine, otherwise, they become computationally intractable; the underlying state variable becomes path-dependent, the tree “splinters,” and the number of distinct nodes goes up exponentially rather than arithmetically as the number of time steps grows. Unfortunately, we have accumulated a great deal of evidence that volatility is time varying, which is a factor that splinters the tree. In this article, Beliaeva and Nawalkha show how to get around the problem by transforming the returns process to create two uncorrelated path-independent trees for returns and variance that can be put together into a single recombining two-dimensional lattice. The procedure is general; here they illustrate its use with the popular Heston model.TOPICS: Options, factor-based models