A sampling-based stochastic programming algorithm and its applications to currency option hedging

This dissertation is intended to study the stochastic optimization of a dynamical currency option hedging process and presents a sampling-based scenario aggregation algorithm which can be used to solve the optimal currency option hedging model.; First, we review various financial applications of stochastic programming modeling techniques in the literature and examine traditional option hedging and valuation methods in finance.; Next, we analyze the uncertain factors in currency exchange and discuss how to generate scenarios and scenario tree for financial optimization methods. We examine the advantages of using short-term derivative securities in portfolio hedging and give valuation models for the short term derivative securities traded in the exchange market. We provide three types of optimal currency option hedging models to satisfy various hedging environment and risk management needs.; To solve the currency option hedging model, we propose a sampling-based stochastic programming algorithm which is based on its corresponding deterministic algorithm. The sample frequencies and a sampled scenario tree will be used to approximate the scenario probabilities and the true scenario tree respectively in the algorithm. We prove that the iteration points will converge with probability one to the true optimal solution asymptotically and show that the accuracy and speed of the algorithm depend on the sample size and error tolerance for each sampled problem in the iterations.; Finally, we present the results of numerical experiments of our option hedging models and sampling-based scenario aggregation algorithm. The computational results for the option hedging models show that our optimal hedging method generates better cost-profit hedging performance compared with traditional hedging methods. The experiments of the sampling algorithm shows that the algorithm can generate good solutions effectively, especially for extremely large-scale stochastic programming problems.