References
- U.M. Ascher, S.J. Ruuth, and B.T.R. Wetton, Implicit–explicit methods for time-dependent partial differential equations, SIAM J. Numer. Anal. 32(3) (1995), pp. 797–823. doi: 10.1137/0732037
- 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), pp. 151–167. doi: 10.1016/S0168-9274(97)00056-1
- L.V. Ballestra and L. Cecere, A fast numerical method to price American options under the Bates model, Comput. Math. Appl. 72 (2016), pp. 1305–1319. doi: 10.1016/j.camwa.2016.06.041
- D.S. Bates, Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche mark options, Rev. Financial Stud. 9 (1996), pp. 69–107. doi: 10.1093/rfs/9.1.69
- G. Beylkin, J.M. Keiser, and L. Vozovoi, A new class of time discretization schemes for the solution of nonlinear PDEs, J. Comput. Phys. 147 (1998), pp. 362–387. doi: 10.1006/jcph.1998.6093
- F. Black and M. Scholes, The pricing of options and corporate liabilities, J. Political Econ. 81 (1973), pp. 637–654. doi: 10.1086/260062
- S.M. Cox and P.C. Matthews, Exponential time differencing for stiff systems, J. Comput. Phys. 176(2) (2002), pp. 430–455. doi: 10.1006/jcph.2002.6995
- Q. Du and W. Zhu, Analysis and applications of the exponential time differencing schemes and their contour integration modifications, BIT Numer. Math. 45 (2005), pp. 307–328. doi: 10.1007/s10543-005-7141-8
- P.A. Forsyth and K.R. Vetzal, Quadratic convergence of a penalty method for valuing American options, SIAM. J. Sci. Comput. 23 (2002), pp. 2096–2123. doi: 10.1137/S1064827500382324
- F.X. Giraldo, J.F. Kelly, and E.M. Constantinescu, Implicit–explicit formulations of a three dimensional nonhydrostatic unified model of the atmosphere, SIAM J. Sci. Comput. 35(5) (2013), pp. B1162–B1194. doi: 10.1137/120876034
- S.L. Heston, A closed-form solution for options with stochastic volatility with applications to bond and currency options, Rev. Financial Stud. 6 (1993), pp. 327–343. doi: 10.1093/rfs/6.2.327
- W. Hundsdorfer and J.G. Verwer, Numerical Solution of Time-Dependent Advection–Diffusion–Reaction Equations, Springer, Berlin, 2003.
- S. Ikonen, Efficient numerical solution of Black–Scholes equation by finite difference method, Licentiate Thesis, Department of Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland, 2003.
- A.K. Kassam and L.N. Trefethen, Fourth-order time stepping for stiff PDEs, SIAM. J. Sci. Comput. 26 (2005), pp. 1214–1233. doi: 10.1137/S1064827502410633
- R.C. Merton, Option pricing when the underlying stocks are discontinuous, J. Financ. Econ. 5 (1976), pp. 125–144. doi: 10.1016/0304-405X(76)90022-2
- B.F. Nielsen, O. Skavhaug, and A. Tveito, Penalty and front-fixing methods for the numerical solution of American option problems, J. Comput. Finance 5 (2002), pp. 69–97. doi: 10.21314/JCF.2002.084
- D.M. Pooley, K.R. Vetzal, and P.A. Forsyth, Convergence remedies for non-smooth payoffs in option pricing, J. Comput. Finance 6 (2003), pp. 25–40. doi: 10.21314/JCF.2003.101
- N. Rambeerich, D. Tangman, A. Gopaul, and M. Bhuruth, Exponential time integration for fast finite element solutions of some financial engineering problems, J. Comput. Appl. Math. 224(2) (2009), pp. 668–678. doi: 10.1016/j.cam.2008.05.047
- S. Salmi, J. Toivanen, and L. Von Sydow, Iterative methods for pricing American options under the Bates model, Int. Conf. Comput. Sci. 18 (2013), pp. 1136–1144.
- S. Salmi, J. Toivanen, and L. VonSydow, An IMEX-scheme for pricing options under stochastic volatility models with jumps, SIAM J. Sci. Comput. 36(5) (2014), pp. B817–B834. doi: 10.1137/130924905
- D. Tangman, A. Gopaul, and M. Bhuruth, Exponential time integration and Chebychev discretisation schemes for fast pricing of options, Appl. Numer. Math. 58 (2008), pp. 1309–1319. doi: 10.1016/j.apnum.2007.07.005
- L. von Sydow, J. Toivanen, and C. Zhang, Adaptive finite differences and IMEX time-stepping to price options under Bates model, Int. J. Comput. Math. 92(12) (2015), pp. 2515–2529. doi: 10.1080/00207160.2015.1072173
- M. Yousuf, Efficient L-stable method for parabolic problems with application to pricing American options under stochastic volatility, Appl. Math. Comput. 213 (2009), pp. 121–136.
- M. Yousuf, A.Q.M. Khaliq, and B. Kleefeld, The numerical approximation of nonlinear Black–Scholes model for exotic path-dependent American options with transaction cost, Int. J. Comput. Math. 89 (2012), pp. 1239–1254. doi: 10.1080/00207160.2012.688115
- M. Yousuf, A.Q.M. Khaliq, and R.H. Liu, Pricing American options under multi-state regime switching with an efficient L- stable method, Int. J. Comput. Math. 92(12) (2015), pp. 2530–2550. doi: 10.1080/00207160.2015.1071799
- R. Zvan, P.A. Forsyth, and K.R. Vetzal, Penalty methods for American options with stochastic volatility, J. Comput. Appl. Math. 91 (1998), pp. 199–218. doi: 10.1016/S0377-0427(98)00037-5