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

Document Type : Original Article

Authors

1 Department of Mathematics, University of Guilan, Rasht, Iran

2 Prof., Department of Mathematics, Allameh Tabataba’i University, Tehran, Iran.

Abstract

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.

Keywords

References

  1. Evans, G., Blackledge, J., & Yardley, P. (2012). Numerical methods for partial differential equations. Springer Science & Business Media.‏
  2. Jeong, D., & Kim, J. (2013). A comparison study of ADI and operator splitting methods on option pricing models.Journal of Computational and Applied Mathematics, (247), 162-171.‏
  3. Karimnejad Esfahani, M., Neisy, A., & De Marchi, S. (2021). An RBF approach for oil futures pricing under the jump-diffusion model.Journal of Mathematical Modeling, 9(1), 81-92.‏
  4. Leveque, R. J. (2007). Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems. Society for Industrial and Applied Mathematics.‏
  5. Marchuk, G. I. (1990). Splitting and alternating direction methods. Handbook of numerical analysis, 1, 197-462.‏
  6. Mohamadinejad, R., Biazar, J., & Neisy, A. (2020). Spread option pricing using two jump-diffusion interest rates. University Politehnica of Bucharest scientific Bulletin-series A-applied mathematics and phusics, 82(1), 171-182.‏
  7. Mohamadinejad, R., Neisy, A., & Biazar, J. (2021). ADI method of credit spread option pricing based on jump-diffusion model. Iranian Journal of Numerical Analysis and Optimization, 11(1), 195-210.‏
  8. Safaei, M., Neisy, A., & Nematollahi, N. (2018). New splitting scheme for pricing American options under the Heston model. Computational Economics, 52(2), 405-420.‏
  9. Suárez-Taboada, M., & Vázquez, C. (2010). A numerical method for pricing spread options on LIBOR rates with a PDE model. Mathematical and computer modelling, 52(7-8), 1074-1080.‏
  10. Unger, A. J. (2010). Pricing index-based catastrophe bonds: Part 1: Formulation and discretization issues using a numerical PDE approach. Computers & geosciences, 36(2), 139-149.‏
  11. Wang, Q., & Zhang, Z. (2019). A stabilized immersed finite volume element method for elliptic interface problems. Applied Numerical Mathematics, 143, 75-87.‏ Doi 10.1016/j.apnum.2019.03.010.
Financial Management Perspective
Volume 12, Issue 38
July 2022
Pages 35-49

Files

Share

How to cite

Statistics