Free Access
Issue
ESAIM: M2AN
Volume 55, Number 3, May-June 2021
Page(s) 913 - 938
DOI https://doi.org/10.1051/m2an/2021012
Published online 05 May 2021
  1. Y. Achdou and O. Pironneau, Computational Methods for Option Pricing. In: Vol. 30 of Frontiers in Applied Mathematics. SIAM, Philadelphia, PA (2005). [Google Scholar]
  2. G. Akrivis, M. Crouzeix and C. Makridadis, Implicit–explicit multistep finite element methods for nonlinear parabolic equations, Report 95-22, University of Rennes (1995). [Google Scholar]
  3. A. Almendral and C.W. Oosterlee, Numerical valuation of options with jumps in the underlying. Appl. Numer. Math. 53 (2005) 1–18. [CrossRef] [Google Scholar]
  4. L. Andersen and J. Andreasen, Jump-diffusion processes: volatility smile fitting and numerical methods for option pricing. Rev. Deriv. Res. 4 (2000) 231–262. [CrossRef] [Google Scholar]
  5. U.M. Ascher, S.J. Ruuth and B.T.R. Wetton, Implicit–explicit methods for time-dependent PDE’s. SIAM J. Numer. Anal. 32 (1995) 797–823. [CrossRef] [Google Scholar]
  6. U.M. Ascher, S.J. Ruuth and R.J. Spiteri, Implicit–explicit Runge-Kutta methods for time-dependent partial differential equations. Appl. Numer. Math. 25 (1997) 151–167. [CrossRef] [MathSciNet] [Google Scholar]
  7. J. Becker, A second order backward difference method with variable steps for a parabolic problem. BIT 38 (1998) 644–662. [Google Scholar]
  8. L. Boen and K.J. in ‘t Hout, Operator splitting schemes for American options under the two-asset Merton jump-diffusion model. Preprint arXiv:1912.06809 (2019). [Google Scholar]
  9. L. Boen, K.J. in ‘t Hout, Operator splitting schemes for the two-asset Merton jump-diffusion model. J. Comput. Appl. Math. 387 (2021) 112309. [Google Scholar]
  10. M. Briani, R. Natalini, G. Russo, Implicit–explicit numerical schemes for jump-diffusion processes, Calcolo 44 (2007) 33–57. [Google Scholar]
  11. W. Chen, X. Wang, Y. Yan and Z. Zhang, A second order BDF numerical scheme with variable steps for the Cahn-Hilliard equation., SIAM J. Numer. Anal. 57 (2019) 495–525. [Google Scholar]
  12. Y.Z. Chen, W.S. Wang and A.G. Xiao, An efficient algorithm for options under Merton’s jump-diffusion model on nonuniform grids. Comput. Econ. 48 (2018) 1–27. [Google Scholar]
  13. Y.Z. Chen, A.G. Xiao and W.S. Wang, An IMEX-BDF2 compact scheme for pricing options under regime-switching jump-diffusion models. Math. Methods Appl. Sci. 42 (2019) 2646–2663. [Google Scholar]
  14. C.C. Christara and N.C. Leung, Analysis of quantization error in financial pricing via finite difference methods. SIAM J. Numer. Anal. 56 (2018) 1731–1757. [Google Scholar]
  15. R. Cont and P. Tankov, Financial Modelling with Jump Processes. Chapman & Hall/CRC, Boca Raton, FL (2004). [Google Scholar]
  16. R. Cont and E. Voltchkova, A finite difference scheme for option pricing in jump diffusion and exponential lévy models. SIAM J. Numer. Anal. 43 (2005) 1596–1624. [CrossRef] [MathSciNet] [Google Scholar]
  17. M. Crouzeix, Une méthode multipas implicite-explicite pour l’approximation des équations d’évolution paraboliques. Numer. Math. 35 (1980) 257–276. [CrossRef] [Google Scholar]
  18. Y. d’Halluin, P.A. Forsyth and G. Labahn, A penalty method for American options with jump diffusion processes. Numer. Math. 97 (2004) 321–352. [Google Scholar]
  19. Y. d’Halluin, P.A. Forsyth and K.R. Vetzal, Robust numerical methods for contingent claims under jump diffusion processes. IMA J. Numer. Anal. 25 (2005) 87–112. [Google Scholar]
  20. L. Feng and V. Linetsky, Pricing options in jump-diffusion models: an extrapolation approach. Oper. Res. 56 (2008) 304–325. [Google Scholar]
  21. P.A. Forsyth and K.R. Vetzal, Quadratic convergence for valuing American options using a penalty method. SIAM J. Sci. Comput. 23 (2002) 2095–2122. [Google Scholar]
  22. J. Frank, W. Hundsdorfer and J.G. Verwer, On the stability of implicit–explicit linear multistep methods. Appl. Numer. Math. 25 (1997) 193–205. [Google Scholar]
  23. B. Gaviraghi, M. Annunziato and A. Borzía, Analysis of splitting methods for solving a partial integro-differential Fokker-Planck equation. Appl. Math. Comput. 294 (2017) 1–17. [Google Scholar]
  24. K.J. in ‘t Hout, Numerical Partial Differential Equations in Finance Explained: An Introduction to Computational Finance. Springer Nature, London (2017). [Google Scholar]
  25. K.J. in ‘t Hout and J. Toivanen, ADI schemes for valuing European options under the Bates model. Appl. Numer. Math. 130 (2018) 143–156. [Google Scholar]
  26. K.J. in ‘t Hout and K. Volders, Stability and convergence analysis of discretizations of the Black-Scholes PDE with the linear boundary condition. IMA J. Numer. Anal. 34 (2014) 296–325. [Google Scholar]
  27. M.K. Kadalbajoo, L.P. Tripathi and A. Kumar, Second order accurate IMEX methods for option pricing under Merton and Kou jump-diffusion model. J. Sci. Comput. 65 (2015) 979–1024. [CrossRef] [Google Scholar]
  28. M.K. Kadalbajoo, A. Kumar and L.P. Tripathi, An efficient numerical method for pricing options under jump diffusion model. Int. J. Adv. Eng. Sci. Appl. Math. 7 (2015) 114–123. [Google Scholar]
  29. M.K. Kadalbajoo, A. Kumar and L.P. Tripathi and A radial basis function based implicit–explicit method for option pricing under jump-diffusion models. Appl. Numer. Math. 110 (2016) 159–173. [Google Scholar]
  30. M.K. Kadalbajoo, L.P. Tripathi and A. Kumar, An error analysis of a finite element method with IMEX-time semidiscretizations for some partial integro-differential inequalities arising in the pricing of American options. SIAM J. Numer. Anal. 55 (2017) 869–891. [Google Scholar]
  31. S.G. Kou, A jump diffusion model for option pricing. Manage. Sci. 48 (2002) 1086–1101. [CrossRef] [Google Scholar]
  32. Y. Kwon and Y. Lee, A second-order finite difference method for option pricing under jump-diffusion models. SIAM J. Numer. Anal. 49 (2011) 2598–2617. [CrossRef] [Google Scholar]
  33. Y. Kwon and Y. Lee, A second-order tridiagonal method for American options under jump-diffusion models. SIAM J. Sci. Comput. 33 (2011) 1860–1872. [Google Scholar]
  34. S.T. Lee and H.W. Sun, Fourth order compact scheme with local mesh refinement for option pricing in jump-diffusion model. Numer. Methods Part. Differ. Equ. 28 (2012) 1079–1098. [Google Scholar]
  35. H.L. Liao, T. Tang and T. Zhou, On energy stable, maximum-principle preserving, second order BDF scheme with variable steps for the Allen-Cahn equation. SIAM J. Numer. Anal. 58 (2020) 2294–2314. [Google Scholar]
  36. A.M. Matache, C. Schwab and T.P. Wihler, Fast numerial solution of parabolic integro-differential equations with applications in finance, IMA preprint series 1954, University of Minnesota (2004). [Google Scholar]
  37. A.M. Matache, T. von Petersdorff and C. Schwab, Fast deterministic pricing of options on Lévy driven assets. ESAIM: M2AN 38 (2004) 37–71. [CrossRef] [EDP Sciences] [Google Scholar]
  38. R.C. Merton, Option pricing when underlying stock returns are discontinuous. J. Fin. Econ. 3 (1976) 125–144. [Google Scholar]
  39. D. Nualart and W. Schoutens, Backward stochastic differential equations and Feynman-Kac formula for Lévy processes, with applications in finance. Bernoulli 7 (2001) 761–776. [Google Scholar]
  40. E. Pindza, K.C. Patidar and E. Ngounda, Robust spectral method for numerical valuation of European options under Merton’s jump-diffusion model. Numer. Methods Part. Differ. Equ. 30 (2014) 1169–1188. [Google Scholar]
  41. J.A. Rad and K. Parand, Pricing American options under jump-diffusion models using local weak form meshless techniques. Int. J. Comput. Math. 94 (2016) 1–27. [Google Scholar]
  42. J.A. Rad and K. Parand, Numerical pricing of American options under two stochastic factor models with jumps using a meshless local Petrov-Galerkin method. Appl. Numer. Math. 115 (2017) 252–274. [Google Scholar]
  43. S.J. Ruuth, Implicit–explicit methods for reaction-diffusion problems in pattern-formation, J. Math. Biol. 34 (1995) 148–176. [Google Scholar]
  44. S. Salmi and J. Toivanen, An iterative method for pricing American options under jump-diffusion models. Appl. Numer. Math. 61 (2011) 821–831. [Google Scholar]
  45. S. Salmi and J. Toivanen, IMEX schemes for pricing options under jump-diffusion models. Appl. Numer. Math. 84 (2014) 33–45. [CrossRef] [Google Scholar]
  46. S. Salmi, J. Tovianen and L. von Sydow, An IMEX-scheme for pricing options under stochastic volatility models with jumps. SIAM J. Sci. Comput. 36 (2014) B817–B834. [Google Scholar]
  47. K. Sato, Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press, Cambridge, UK (1999). [Google Scholar]
  48. J.C. Strikwerda, Finite Difference Schemes and Partial Differential Equations. SIAM, Philadelphia (2004). [Google Scholar]
  49. D. Tavella and C. Randall, Pricing Financial Instruments: The Finite Difference Method. John Wiley & Sons, Chichester, UK (2000). [Google Scholar]
  50. J. Toivanen, Numerical valuation of Europen and American options under Kou’s jump-diffusion model. SIAM J. Sci. Comput. 4 (2008) 1949–1970. [Google Scholar]
  51. J.M. Varah, Stability restrictions on second order, three-level finite-difference schemes for parabolic equations. SIAM J. Numer. Anal. 17 (1980) 300–309. [Google Scholar]
  52. J.G. Verwer, J.G. Blom and W. Hundsdorfer, An implicit–explicit approach for atmospheric transport-chemistry problems. Appl. Numer. Math. 20 (1996) 191–209. [Google Scholar]
  53. W.S. Wang and Y.Z. Chen, Fast numerical valuation of options with jump under Merton’s model. J. Comput. Appl. Math. 318 (2017) 79–92. [Google Scholar]
  54. D. Wang and S.J. Ruuth, Variable step-size implicit–explicit linear multistep methods for time-dependent partial differential equations. J. Comput. Math. 26 (2008) 838–855. [Google Scholar]
  55. W.S. Wang, Y.Z. Chen and H. Fang, On the variable two-step IMEX BDF method for parabolic integro-differential equations with nonsmooth initial data arising in finance. SIAM J. Numer. Anal. 57 (2019) 1289–1317. [Google Scholar]
  56. W.S. Wang, M.L. Mao and Z. Wang, Stability and error estimates for the variable step-size BDF2 method for linear and semilinear parabolic equations. Adv. Comput. Math. 47 (2021) 1–28. [Google Scholar]
  57. X.L. Zhang, Numerical analysis of American option pricing in a jump-diffusion model. Math. Oper. Res. 22 (1997) 668–690. [CrossRef] [Google Scholar]
  58. K. Zhang and S. Wang, A computational scheme for options under jump-diffusion processes. Int. J. Numer. Anal. Model. 6 (2009) 110–123. [Google Scholar]

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