New Results on Deterministic Pricing of Financial Derivatives

Monte Carlo simulation is widely used to price complex financial instruments. Recent theoretical results and extensive computer testing indicate that deterministic methods may be far superior in speed and confidence. In this paper we test the generalized Faure method due to Tezuka on a Collateralized Mortgage Obligation (CMO). This requires integration in 360 dimensions. We conclude that deterministic methods beat Monte Carlo by a wide margin. Among the deterministic methods we have tested, the generalized Faure method is the method of choice. For example, for the hardest CMO tranche, generalized Faure achieves accuracy 10$^{-2}$ with just 170 points while the Monte Carlo method requires 2700 points for the same accuracy. We introduce a new and more rigorous definition of speed-up. For high accuracy, generalized Faure is 1000 times faster than Monte Carlo.