Pricing Options by the Local Differential Quadrature Method
Date Issued
2011
Date
2011
Author(s)
Sun, Chia-Peng
Abstract
This study demonstrates the numerical procedure of solving option-pricing problems by the local differential quadrature (LDQ) method. After the remarkable contribution of Black, Scholes and Merton in 1973, many option-pricing models are developed for relaxing the restrictions of the Black-Scholes (BS) model or extending the theory to much wider applications. In general, these models can be divided into two kinds based on the assumption of the dynamic process for the underlying assets. Ones are diffusion models in which the dynamics of the underlying-asset price follow the Brownian process; the others are jump-diffusion models with the random jumps considered in the dynamics. Our work aims to develop a numerical process for solving both the diffusion and jump-diffusion models efficiently. Because of the non-differentiability of the payoff functions, non-uniformly distributed nodes are applied, and thus the LDQ method is used due to its advantage for arbitrary grid nodes. For the jump-diffusion models, we also provide an efficient scheme for computing the non-local integral of the governing equations on the non-uniform nodal girds. Numerical experiments include typical option-pricing problems, such as European, American, lookback, binary and barrier options. According to the comparison with the reference data, our results show that the proposed method has robustness and good performance for both diffusion and jump-diffusion type option-pricing models. In brief, one can conclude that it is a successful application.
Subjects
local differential quadrature
the Black-Scholes model
jump-diffusion model
European option
American option
lookback option
barrier option
Type
thesis
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