A Forward Shooting Grid Method for Option Pricing with Stochastic Volatility

One of the most common sources of path dependency in derivatives arises when the volatility is stochastic. This is apparent in the basic binomial model, where time-varying volatility causes the lattice to splinter rather than recombine, leading to <i>n</i>² different nodes at the nth time step instead of <i>n</i> + 1 nodes in a tree that recombines. Various methods have been developed to deal with that problem within a lattice framework, by constructing three-dimensional lattices with both the price and the volatility as state variables. An alternative technique is the forward shooting grid that builds a lattice for the stock price and carries along a set of possible values for the volatility at each price node as auxiliary variables. But both of those approaches can run into problems with negative transition probabilities and difficulty in achieving the right correlation between returns and volatility changes. In this article, Costabile, Massabó, and Russo develop a different forward shooting grid approach, in which the squared volatility is the primary path-dependent variable and stock prices are carried along as the auxiliary variables. Negative transition probabilities are avoided, and the procedure produces highly accurate results very efficiently in a compact tree. <b>TOPICS:</b>Options, statistical methods, volatility measures