References
- L.B.G. Andersen and V.V. Piterbarg, Moment explosions in stochastic volatility models, Finance Stoch. 11 (2007), pp. 29–50. doi: 10.1007/s00780-006-0011-7
- I.J. Clark, Foreign Exchange Option Pricing: A Practitioner's Guide, John Wiley & Sons, Chichester, 2011.
- J.C. Cox, J.E. Ingersoll, and S.A. Ross, A theory of the term structure of interest rates, Econometrica 53 (1985), pp. 385–407. doi: 10.2307/1911242
- B. Dupire, Pricing with a smile, Risk January (1994), pp. 18–20.
- B. Engelmann, F. Koster, and D. Oeltz, Calibration of the Heston stochastic local volatility model: A finite volume scheme, 2012. Available at SSRN 1823769.
- F. Fang and C.W. Oosterlee, A novel pricing method for European options based on Fourier-cosine series expansions, SIAM J. Sci. Comput. 31 (2008), pp. 826–848. doi: 10.1137/080718061
- F. Fang and C.W. Oosterlee, A Fourier-based valuation method for Bermudan and barrier option under Heston's model, SIAM J. Financ. Math. 2 (2011), pp. 439–463. doi: 10.1137/100794158
- J. Gatheral and A. Jacquier, Arbitrage-free SVI volatility surfaces, Quant. Financ. 14 (2014), pp. 59–71. doi: 10.1080/14697688.2013.819986
- I. Gyöngy, Mimicking the one-dimensional marginal distributions of processes having an Ito differential, Probab. Theory Related Fields 71 (1986), pp. 501–516. doi: 10.1007/BF00699039
- T. Haentjens and K.J. in 't Hout, Alternating direction implicit finite difference schemes for the Heston–Hull–White partial differential equation, J. Comput. Financ. 16 (2012), pp. 83–110. doi: 10.21314/JCF.2012.244
- P. Henry-Labordère, Calibration of local stochastic volatility models to market smiles, Risk September (2009), pp. 112–117.
- V.E. Henson and U.M. Yang, BoomerAMG: A parallel algebraic multigrid solver and preconditioner, Appl. Numer. Math. 41 (2002), pp. 155–177. doi: 10.1016/S0168-9274(01)00115-5
- S.L. 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
- K.J. in 't Hout and S. Foulon, ADI finite difference schemes for option pricing in the Heston model with correlation, Int. J. Numer. Anal. Model 7 (2010), pp. 303–320.
- K.J. in 't Hout and C. Mishra, Stability of ADI schemes for multidimensional diffusion equations with mixed derivative terms, Appl. Numer. Math. 74 (2013), pp. 83–94. doi: 10.1016/j.apnum.2013.07.003
- K.J. in 't Hout and B.D. Welfert, Stability of ADI schemes applied to convection–diffusion equations with mixed derivative terms, Appl. Numer. Math. 57 (2007), pp. 19–35. doi: 10.1016/j.apnum.2005.11.011
- K.J. in 't Hout and B.D. Welfert, Unconditional stability of second-order ADI schemes applied to multi-dimensional diffusion equations with mixed derivative terms, Appl. Numer. Math. 59 (2009), pp. 677–692. doi: 10.1016/j.apnum.2008.03.016
- K.J. in 't Hout and M. Wyns, Convergence of the Hundsdorfer–Verwer scheme for two-dimensional convection–diffusion equations with mixed derivative term, AIP Conf. Proc. 1648 (2015), pp. 850054-1–850054-5.
- W. Hundsdorfer, Accuracy and stability of splitting with stabilizing corrections, Appl. Numer. Math. 42 (2003), pp. 213–233. doi: 10.1016/S0168-9274(01)00152-0
- W. Hundsdorfer and J.G. Verwer, Numerical Solution of Time-Dependent Advection–Diffusion–Reaction Equations, Springer, Berlin, 2003.
- A. Lipton, The vol smile problem, RISK February (2002), pp. 61–65.
- D.M. Pooley, K.R. Vetzal, and P.A. Forsyth, Convergence remedies for non-smooth payoffs in option pricing, J. Comput. Financ. 6 (2003), pp. 25–40. doi: 10.21314/JCF.2003.101
- R. Rannacher, Finite element solution of diffusion problems with irregular data, Numer. Math. 43 (1984), pp. 309–327. doi: 10.1007/BF01390130
- Y. Ren, D. Madan, and M.Q. Qian, Calibrating and pricing with embedded local volatility models, Risk September (2007), pp. 138–143.
- H. Risken, The Fokker-Planck Equation: Methods of Solution and Applications, 2nd ed., Springer, Berlin, 1989.
- M.J. Ruijter and C.W. Oosterlee, Two-dimensional Fourier cosine series expansion method for pricing financial options, SIAM J. Sci. Comput. 34 (2012), pp. B642–B671. doi: 10.1137/120862053
- R. Tachet, Non-parametric model calibration in finance, Ph.D. thesis, Ecole Centrale Paris, 2011.
- G. Tataru and T. Fisher, Stochastic local volatility, Technical report, Bloomberg, 2010.
- D. Tavella and C. Randall, Pricing Financial Instruments: The Finite Difference Method, John Wiley & Sons, New York, 2000.
- A.W. van der Stoep, L.A. Grzelak, and C.W. Oosterlee, The Heston stochastic-local volatility model: Efficient Monte Carlo simulation, Int. J. Theor. Appl. Finance 17 (2014), pp. 1450045-1–1450045-30. doi: 10.1142/S0219024914500459
- J.G. Verwer, E.J. Spee, J.G. Blom, and W. Hundsdorfer, A second-order Rosenbrock method applied to photochemical dispersion problems, SIAM J. Sci. Comput. 20 (1999), pp. 1456–1480. doi: 10.1137/S1064827597326651
- M. Wyns, Convergence analysis of the Modified Craig–Sneyd scheme for two-dimensional convection–diffusion equations with nonsmooth initial data, to appear in IMA J. Numer. Anal. (2016). doi: 10.1093/imanum/drw028.