SPREAD OPTION PRICING USING TWO JUMP-DIFFUSION INTEREST RATES

Nowadays, as the financial markets grow larger, to compare with the past, financial investments and their modeling become more complicated. One of the difficulties in these financial modeling is selecting an appropriate model for interest rate. The main reason is that, in real market some data goes under sudden changes in some points so, they may not be in complete harmony with our selected model. As a result many questions come to existence, putting our choice under question mark. Thus, studying and analyzing the interest rate model that has jump-diffusion terms is of great importance. In this paper, we assume the spread options are based on two LIBOR interest rates, while one of them follows a geometric Brownian motion (GBM) with jump-diffusion terms. As the aim of our work, is to find a suitable model for pricing the spread options, first, we attempt to achieve a partial integro-differntial equation (PIDE) which determine the price of the options, regarding initial and boundary conditions. Then a generalized alternating direction implicit (ADI) method with a proper stepsize is proposed in order to solve our model. The reader should note, this is due to reason that there is no closed form, solution for our model. Eventually, MATLAB software is used to implement the ADI method using data that fits the model. In addition, to illustrate the simplicity and reliability of the proposed approach some examples are provided in the last chapter of this paper.