For the evaluation of European options with constant local volatility, a general closed-form solution was given by the Black-Scholes formula. In practice, such local volatility may vary, thus the Black-Scholes formula does not work efficiently. A common way to deal with such problem is to apply numerical methods, particularly the Finite Element Method. The use of Galerkin Least Square stabilization method combined with adaptive mesh refinements is explored for bad scenarios having large local volatility, which was described by the Constant Elasticity of Variance model. We implement our numerical schemes in Matlab and observe the accuracy of our numerical solutions. Finally, we take advantage of better ways to discretize our domain with geometric partition to achieve high accuracy.
Worcester Polytechnic Institute
Major Qualifying Project
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