Pricing Moving-Average-Lookback Options

This thesis investigates computational methods for pricing complex path-dependent derivative securities, especially geometricand arithmetic-moving-average-lookback options. The latter security was rst issued by Polaris Securities in 1999. Our methodology can be easily modi ed to price similarly structured options issued by other securities rms. The moving-average-lookback option is a call option struck at the minimummoving average of underlying asset price. We consider both geometric averaging and the much harder arithmetic averaging used by Polaris. The pricing results show that our algorithms on the CRR model converge quickly to the correct value. We also nd that the price di erence between geometric averaging and arithmetic averaging is slight. As it takes much less time to price the geometric-moving-average version, it serves as a good approximation to the arithmetic-moving-average version. The least-squares simulation, introduced by Longsta and Schwartz (2001), can be applied to price American-style moving-average-lookback options. Compared with our algorithms, the least-squares approach systematically undervalues the options. When applied to the two arithmetic-moving-average-lookback options issued by Polaris Securities in 1999, our algorithm prices them almost exactly. The numerical delta and gamma of the options are also investigated.