Valuing American Options Using Fast Recursive Projections
67 Pages Posted: 2 Jun 2016
Date Written: June 1, 2016
We introduce a fast and widely applicable numerical pricing method that uses recursive projections. The method is based on a simple grid sampling of value functions and state-price densities. Numerical illustrations with different American and Bermudan payoffs with dividend paying stocks in the Black Scholes and Heston models show that the method is fast, accurate, and general.
We find that the early exercise boundary of an American call option on a discrete dividend paying stock is higher under the Merton and Heston models than under the Black-Scholes model, as opposed to the continuous dividend case. A large database of call options on stocks with quarterly dividends shows that adding stochastic volatility and jumps to the Black-Scholes benchmark reduces the amount foregone by call holders failing to optimally exercise by 25%. Transaction fees cannot fully explain the suboptimal behavior.
Keywords: Option pricing, American option, Bermudan option, discrete transform, discrete dividend paying stock, suboptimal non-exercise, numerical techniques
JEL Classification: G13, C63
Suggested Citation: Suggested Citation