Document Type masters report Author Name LeRay, David Email Address daveleray at gmail.com URN etd-050907-133817 Title Efficient Pricing of an Asian Put Option Using Stiff ODE Methods Degree MS Department Mathematical Sciences Advisors Homer Walker, Advisor Keywords option financial mathematics differential equation stiff Date of Presentation/Defense 2007-05-09 Availability unrestricted
Financial mathematics is a branch of mathematics that assesses the risk and value of various financial instruments. Banks, companies, and other institutions mitigate their risk through financial instruments known as derivatives,that derive their value from some underlying asset. The equations that arise from pricing and modeling can be very complex, leading to the necessity of numerical methods.
This project studied the use of certain numerical methods for the pricing of a particular type of option called an Asian option. Asian options can provide favorable risk profiles because the payout is determined based on the average value over a time period, rather than the final value. The price of an Asian option is governed by a partial differential equation in three variables: stock price, average price over the current time interval, and time.
The solution method was first to discretize the partial differential equation into a system of ordinary differential equations. Next, the ODE system was integrated using a stiff-ODE solver available in MATLAB. Enhancements to this solution method include specifying the sparsity pattern, implementing an iterative linear solver (GMRES) in place of MATLAB's built-in direct linear solver, and using preconditioning to improve the solution characteristics of that solver.
Files dleray1.pdf dleray2.pdf dleray3.pdf
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