Advancing the quadrature method in option pricing - Su, Haozhe (2018)
This thesis advances the research on the quadrature (QUAD) method. We aim to make it more computationally efficient, apply it to different underlying processes and even develop a new breed of QUAD method. QUAD is efficient in many ways except when it comes to options with early exercise opportunities such as Bermudan or American options. We develop a series of acceleration techniques for the QUAD method to improve its implementation. After that, we show how to apply the accelerated QUAD method to pricing American options under lognormal jump diffusion and stochastic volatility jump diffusion processes. QUAD is more efficient in dealing with jump processes compared with other numerical techniques such as the finite difference method and the Monte Carlo method, as long as the transition probability density of those processes are known. When the transition probability density is not known in closed-form, this thesis explores a new approach by combining the finite difference method with QUAD (FD-QUAD) – since density can be calculated numerically using the finite difference methods. Overall, this thesis greatly improves and advances the quadrature method in option pricing.