Spread Option Pricing Based on Two Jump-diffusion Libor Interest Rate Models

Nowadays, financial derivatives play an important role in the development of financial markets and risk management. Financial derivatives markets are not only a tool for risk management but also a secondary market to attract small capital for implementing large projects. Countries with extremely volatile financial markets need some novel financial risk management tools. In this paper, the spread option is used as a tool for investment and risk management. First, we obtain a model by using stochastic differential equations and partial differential equations. Then the model derived from a stochastic differential equation with a jump term is transformed into a risk-free integral partial differential equation which represents the spread option price on the Libor interest rates since the model does not have a closed-form solution or analytical solution, the solution is estimated at discrete points by using the alternating direction implicit (ADI) method. The stability of the method is also proved. In the next step, the pricing model is implemented in MATLAB software and the results are illustrated. Finally, it is concluded that the ADI method is an efficient and appropriate method that solves the problems in pricing models caused by jumps.