The Dimension-Reduction Methods For Pricing Options On The Minimum Of Two Average Prices

Options on the minimum of two average prices are promising new compound options in financial markets. This thesis studies the valuation of options on the minimum of two average prices. The average price includes the geometric mean and arithmetic mean. We provide a closed-form pricing formula for the option on the minimum of two geometric average prices involving stock dividends. The pricing problem of the option on the minimum of two arithmetic average prices is a four-dimensional problem. Therefore a dimension-reduction technique is developed to reduce the four-dimensional problem to a two-dimensional one.