Pricing American Options in the Heston Model: A Close Look on Incorporating Correlation

Abstract

The Binomial model and similar lattice methods are workhorses of practical derivatives valuation. But returns processes more realistic than lognormal diffusions with constant parameters easily create difficulties for them. One of the most important extensions of the Black-Scholes paradigm is to allow stochastic volatility, but even nonstochastic timevarying volatility destroys the important property that the tree recombines, which limits the growth in the number of nodes as time advances. Stochastic volatility introduces a second random variable, which then requires adding another dimension to the tree, under the constraint that the return and volatility changes must maintain the same degree of correlation as in the data. The Heston model features correlation in return and volatility shocks, but building it into a lattice is tricky. In this article, Ruckdeschel, Sayer, and Szimayer develop a lattice method that begins with a binomial tree for the volatility and a trinomial tree for stock price, and then connects them in such a way that the empirical degree of correlation between return and volatility is maintained. Efficiency relative to existing methods is increased, and in some cases it is possible to improve performance further by matching higher moments as well.