References
- W. Allegretto, Y. Lin and H. Yang, Finite element error estimates for a nonlocal problem in American option valuation, SIAM J. Numer. Anal. 39 (2001), pp. 834–857. doi: 10.1137/S0036142900370137
- N. Beliaeva and S. Nawalkha, A simple approach to pricing American options under the Heston stochastic volatility model, J. Derivatives 17(4) (2010), pp. 25–43. doi: 10.3905/jod.2010.17.4.025
- J. Cai and H. Yang, A mixed Monte Carlo method for the European options under several two-factor models, working paper, 2017.
- P. Carr and M. Chesney, American put call symmetry, preprint, (1996).
- N. Clarke and K. Parrott, Multigrid for American option pricing with stochastic volatility, Appl. Math. Finance 5(3) (1999), pp. 177–195. doi: 10.1080/135048699334528
- R. Cont, Empirical properties of asset returns: Stylized facts and statistical issues, Quant. Finance 1 (2001), pp. 223–236. doi: 10.1080/713665670
- J.C. Cox, J.E. Ingersoll and S.A. Ross, A Theory of the term structure of interest rates, Econometrica, 53 (1985), pp. 385–408. doi: 10.2307/1911242
- J. Detemple, American options: Symmetry properties, Option pricing, interest rates and risk management (2001), Cambridge University Press, Cambridge, UK, pp. 67–104.
- F. Fang and C.W. Oosterlee, A Fourier-based valuation method for Bermudan and barrier options under Heston model, SIAM J. Finan. Math. 2 (2011), pp. 439–463. doi: 10.1137/100794158
- J. Gatheral, The Volatility Surface: A Practitioner's Guide, Wiley Finance, New York, 2006.
- P. Glasserman, Monte Carlo Methods in Financial Engineering, Springer-Verlag, New York, 2004.
- S.T. Haentjens and K.J. in 't Hout, ADI schemes for pricing American options under the Heston model, Appl. Math. Finan. 22 (2015), pp. 207–237. doi: 10.1080/1350486X.2015.1009129
- S. Heston, A closed-form solution for options with stochastic volatility with applications to bond and currency options, Rev. Financ. Stud 6 (1993), pp. 327–343. doi: 10.1093/rfs/6.2.327
- S. Ikonen and J. Toivanen, Operator splitting methods for pricing American options under stochastic volatility, Numer. Math. 113 (2009), pp. 299–324. doi: 10.1007/s00211-009-0227-5
- P. Kovalov, V. Linetsky and M. Marcozzi, Pricing multi-asset American options: A finite element method-of-lines with smooth penalty, J. Sci. Compu. 33(3) (2007), pp. 209–237. doi: 10.1007/s10915-007-9150-z
- D.P. Leisen, Stock evolution under stochastic volatility: A discrete approach, J. Derivatives Winter (2000), pp. 9–27. doi: 10.3905/jod.2000.319146
- S. Levendorskii, Efficient pricing and reliable calibration in the Heston model, Int. J. Theor. Appl. Finan. 15 (2012), pp. 1250050. doi: 10.1142/S0219024912500501
- G. Loeper and O. Pironneau, A mixed PDE/Monte-Carlo method for stochastic volatility models, C. R. Acad. Sci. Paris, I 347 (2009), pp. 559–563. doi: 10.1016/j.crma.2009.02.021
- F.A. Longstaff and E.S. Schwartz, Valuing American options by simulation: A simple least-squares approach, Rev. Finan. Stud. 14 (2001), pp. 113–147. doi: 10.1093/rfs/14.1.113
- C.W. Oosterlee, On multigrid for linear complementarity problems with application to American-style options, Elec. Trans. Numer. Anal. 15 (2003), pp. 165–185.
- J. Persson and L. von Sydow, Pricing American options using a space-time adaptive finite difference method, Math. Comp. Simul. 80 (2010), pp. 1922–1935. doi: 10.1016/j.matcom.2010.02.008
- P. Ritchken and R. Trevor, Pricing options under generalized GARCH and stochastic volatility process, J. Finan. 54(N1) (1999), pp. 377–402. doi: 10.1111/0022-1082.00109
- H. Stoll, The relationship between put and call option prices, J. Finan. 24(5) (1969), pp. 801–824. doi: 10.1111/j.1540-6261.1969.tb01694.x
- M. Vellekoop and H. Nieuwenhuis, A tree-based method to price American options in the Heston model, J. Comp. Finan. 13 (2009), pp. 1–21. doi: 10.21314/JCF.2009.197
- 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