EEP-Collocation Methods For Pricing American Strangle Options

Problems of pricing American options have been widely studied in the literature. Since American options can be exercised at any time before maturity. the pricing problem is much more difficult than that for European options.In addition American options may have many variants, which make the pricing problems rather complex. This thesis studies the pricing problems for a typical American strangle option.The value of the American strangle option can be expressed as an EEP form, which is that the option value equals to the value of European strangle option plus the early exercise premium. The EEP form leads to a system of nonlinear singular Volterra integral equations that determines the early exercise boundaries.Although in the literature some authors have developed methods to solve the pricing problems for American strangles (e.g., Chiarella and Ziogas (2005)), their methods are not easy to implement and present a lower-order convergence.This thesis develops a collocation method based on the high-order polynomials, which are widely used in the numerical solutions of integral equations, to solve the system of integral equations that the early exercise boundaries satisfy. The numerical solutions give the approximate values of early exercise boundaries and are further used to calculate the value of options.Numerical examples are provided to verify the high-accuracy and the ease of implementations of our methods by comparing with the existing methods in the literature. One additional advantage of our methods is that the numerical solutions have high-order smoothness on the mesh nodes, which makes the calculation of Greeks easier and more reliable.