Stochastic dynamic programming: Monte Carlo simulation and applications to finance.

摘要

Stochastic dynamic programming provides a rich modeling framework for tackling sequential decision-making problems under uncertainty. In this dissertation, which consists of three essays, we consider numerical techniques for solving stochastic dynamic programming models, particularly as applied to the pricing of American-style derivatives in finance.; In the first essay, we consider two simulation-based stochastic dynamic programming algorithms for the pricing of multi-dimensional American-style options. Specifically, we extend recently proposed single-dimensional pricing methods to the American-Asian option and the American max option on the maximum of multiple assets. In numerical experiments, our extensions indicate superior pricing performance as compared with previously proposed extensions.; In the second essay, we present a new approach to pricing single-dimensional American-style derivatives that is applicable to any Markovian setting (i.e., not limited to geometric Brownian motion) for which European call option prices are readily available. By approximating the value function with an appropriately chosen interpolation function, the pricing of an American-style derivative with arbitrary payoff function is converted to the pricing of a portfolio of European call options, leading to analytical expressions for those cases where analytical European call prices are available. In many settings, the approach yields upper and lower analytical bounds that converge to the true derivative price. We provide computational results on American-style put and call options in the geometric Brownian motion and jump-diffusion settings. Further, using Fast Fourier Transform technology to compute the European call option prices, we empirically compare American-style put option prices from three pure jump models calibrated to a common S&P 500 data set. Lastly, we extend our methods to the American-Asian option and show that the pricing of this multi-dimensional derivative can also be converted to the pricing of European call options.; In the third essay, we propose a resource allocation procedure for solving stochastic dynamic programming problems with deterministic state transitions and relatively small state and action spaces when the cost functions are not explicity available and can only be sampled (e.g., using simulation), but the sampling budget is limited. Numerical results indicate that our method has the potential to significantly enhance computational efficiency.