Hilbert Transform Methods in Financial Engineering

点击翻译按钮获取中文摘要

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5)This grant provides funding for the development of a high performance computational method for the fast and accurate pricing of various option contracts with non-standard payoffs. The proposed research results will be used to price such option contracts in stochastic volatility and jump models which relax the restrictive assumptions of the widely used Black-Scholes-Merton model. A method based on the Hilbert transform will be used to price Bermudan style vanilla, lookback and barrier options in pure jump Levy process models, certain Asian equity and interest rate options in square root models, as well as option contracts in multi-asset models. The method will also be applied to efficiently invert an analytic characteristic function to obtain the cumulative distribution function of a random variable, and to simulate pure jump Levy processes and processes with stochastic volatilities. Option contracts are widely used by corporations and fund managers to hedge against financial risks they face due to the fluctuation of interest rates, currency exchange rates, and equity prices. Many option contracts have complicated payoffs, depending on the maximum, minimum, or average of the underlying financial variable, to satisfy specific hedging requirements. Most option contracts can be exercised before their maturities. The commonly used Black-Scholes-Merton option pricing model significantly underestimates risks that are associated with these derivative products. If successful, the results of the proposed research will lead to accurate and efficient pricing of many important classes of option contracts when risks associated with the underlying financial variables are modeled in more appropriate ways. The research results will also contribute to various application areas in applied probability, engineering, and economics.