Research ArticleOpen AccessGoogle Scholar indexed
An Implicit-Explicit Computational Method Based on Time Semi-Discretization for Pricing Financial Derivatives with Jumps
School of Economic, Jinan University, Guangzhou, China
- 1 School of Economic, Jinan University, Guangzhou, China
Open Journal of Statistics·Volume 08 (2018)·Pages 334–344·Published 30 March 2018·DOI10.4236/ojs.2018.82022
Copy link · social · email
Abstract
This paper considers pricing European options under the well-known of SVJ model of Bates and related computational methods. According to the no-arbitrage principle, we first derive a partial differential equation that the value of any European contingent claim should satisfy, where the asset price obeys th e SVJ model. This equation is numerically solved by using the implicit - explicit backward difference method and time semi-discretization. In order to explain the validity of our method, the stability of time semi-discretization scheme is also proved. Finally, we use a simulation example to illustrate the efficiency of the method.
KeywordsSVJ Model of BatesTime Semi-DiscretizationStabilityNo-Arbitrage PrincipleImplicit-Explicit Backward Difference Method
- Black, F. and Scholes, M. (1973) The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81, 637-659. https://doi.org/10.1086/260062
- Merton, R.C. (1976) Option Pricing when Underlying Stock Returns Are Discontinuous. Journal of Financial Economics, 3, 125-144. https://doi.org/10.1016/0304-405X(76)90022-2
- Xu, W., Wu, C., Xu, W. and Li, H. (2002) A Jump-Diffusion Model for Option Pricing under Fuzzy Environments. Management Science, 48, 1086-1101. https://doi.org/10.1287/mnsc.48.8.1086.166
- Hull, J. and White, A. (1987) The Pricing of Options on Assets with Stochastic Volatilities. The Journal of Finance, 42, 281-300. https://doi.org/10.1111/j.1540-6261.1987.tb02568.x
- Heston, S.L. (1993) A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options. Review of Financial & Studies, 6, 327-343. https://doi.org/10.1093/rfs/6.2.327
- Almendral, A. and Oosterlee, C.W. (2005) Numerical Valuation of Options with Jumps in the Underlying. Applied Numerical Mathematics, 53, 1-18. https://doi.org/10.1016/j.apnum.2004.08.037
- Ngounda, E., Patidar, K.C. and Pindza, E. (2013) Contour Integral Method for European Options with Jumps. Communications in Nonlinear Science & Numerical Simulation, 18, 478-492. https://doi.org/10.1016/j.cnsns.2012.08.003
- D’Halluin, Y., Forsyth, P.A. and Vetzal, K.R. (2003) Robust Numerical Methods for Contingent Claims under Jump Diffusion Processes. IMA Journal of Numerical Analysis, 25, 87-112.
- Kwon, Y. and Lee, Y. (2011) A Second-Order Finite Difference Method for Option Pricing under Jump-Diffusion Models. SIAM Journal on Numerical Analysis, 49, 2598-2617. https://doi.org/10.1137/090777529
- Ascher, U.M., Ruuth, S.J. and Spiteri, R.J. (1997) Implicit-Explicit Runge-Kutta Methods for Time-Dependent Partial Differential Equations. Elsevier Science Publishers B. V. https://doi.org/10.1016/S0168-9274(97)00056-1
- Kadalbajoo, M.K., Kumar, A. and Tripathi, L.P. (2016) A Radial Basis Function Based Implicit-Explicit Method for Option Pricing under Jump-Diffusion Models. Applied Numerical Mathematics, 110, 159-173. https://doi.org/10.1016/j.apnum.2016.08.006