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Options As Free Boundary Problems
On behalf of the Department of Mathematics and Statistics of the College of Arts and Sciences, you are cordially invited on a seminar to be conducted by Dr. Ghada Alobaidi, Associate Professor in Mathematics and Statistics, AUS.
A financial derivative such as an option is a contract whose value depends on the values of an underlying asset such as a stock, a currency or a commodity. Derivatives provide a good way to manage the risk associated with changes in the value of the underlying asset. The question is what is the fair value of an option? The question is answered by Black-Scholes formula for the option price.
Following this overview, I will briefly discuss my research on American call options whose value is described by the Black-Scholes PDE together with a constraint that arises from the possibility of early exercise which leads to a free boundary problem for the optimal exercise boundary. As an exact solution has yet to be found, I use asymptotic techniques to find a series solution for the location of the optimal exercise boundary and the value of the option near to expiration.
For further details, kindly contact [email protected].