A New Approach for Computing Option Prices of the Hull-White Type with Stepwise Reversion and Volatility Functions

Interest rate models, starting with Vasicek, generally include mean-reversion toward a long term level. As such models were applied in the real world to price interest-dependent instruments, including derivatives, they were extended in order to match observed market prices. One way is to introduce more stochastic factors, but the other is to introduce mean-reversion and other kinds of nonstochastic time variation for important parameters, notably volatility. Incorporating such flexibility into a single stochastic factor interest rate lattice requires some method of discretizing these functions, and it is not always easy. In this article, Jin, Gotoh and Sumita develop a new technique involving the use of Ehrenfest functions to approximate mean-reverting O-U processes. Performance of their approach is comparable to a trinomial tree, but it has the advantage of being operational for parameter values for which a trinomial breaks down. It may also facilitate pricing of more complex instruments, with barriers and other such features.