Doctor of Philosophy (PhD)
First Committee Member
Second Committee Member
Third Committee Member
Fourth Committee Member
Fifth Committee Member
Number of Pages
Pricing options under multi-factor models are challenging and important problems for ﬁnancial applications. In particular, the closed form solutions are not available for the American options and some European options, and the correlations between factors increase the complexity and diﬃculty for the formulations and implements of the numerical methods.
In this dissertation, we ﬁrst introduce a general transformation to decouple correlated stochastic processes governed by a system of stochastic diﬀerential equations. Then we apply the transformation to the popular two-factor models: the two-asset model, the stochastic volatility model, and the stochastic interest rate models. Based on our new formulations, we develop a mixed Monte Carlo method, a lattice method, and a ﬁnite volume-alternating direction implicit method for pricing the European and American options under these models. The proposed methods can be easily implemented and need less memory. Numerical results are also presented to validate our C++ programs and to examine our methods. It shows that our methods are very accurate and eﬃcient.
Decoupling; Finite volume - alternating direction implicit method; Lattice method; Mixed Monte Carlo method; Option pricing; Two-factor models
Applied Mathematics | Corporate Finance | Finance | Finance and Financial Management | Mathematics
Cai, Jiacheng, "Numerical Methods for Option Pricing under the Two-Factor Models" (2017). UNLV Theses, Dissertations, Professional Papers, and Capstones. 3072.