Abdul Khaliq
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MATHEMATICS COLLOQUIUM
Speaker: Abdul Khaliq Abstract. The development of modern option pricing began with the publication of the Black Scholes option pricing formula in 1973. Black & Scholes (1973) and Merton (1973) gave a derivation of a model equation to compute the values of a European Option. This equation has had such financial impact that Robert Merton and Myron Scholes shared the 1997 Nobel Prize for economics (Fisher Black having died in 1995). The Black Scholes formula computes the value of a European option based on the underlying asset, strike price, volatility of the asset, and the time until the option expires. The European option can be exercised only at expiry date whereas and American option has an additional feature that exercise is permitted at any time during the life of the option. Therefore, pricing of an American option is more complicated since at each time we have to determine not only the option value but also whether or not it should be exercised (early exercise constraint). In this talk we will discuss linearly implicit methods, their efficient implementation, and strong stability properties for American options. Our approach transforms the free boundary problem into a nonlinear partial differential equation by adding a continuous penalty term into Black-Scholes model. Numerical experiments will be demonstrated and future directions for multi asset problems will be discussed. |