Asymptotic expansion method for pricing and hedging American options with two-factor stochastic volatilities and stochastic interest rate

References

• A. Agarwal, S. Juneja, and R. Sircar, American options under stochastic volatility: Control variates, maturity randomization and multiscale asymptotics, Quant. Finance 16 (2016), pp. 17–30. doi: 10.1080/14697688.2015.1068443
   Web of Science ®Google Scholar
• F. AitSahlia, M. Goswami, and S. Guha, Are There Critical Levels of Stochastic Volatility for Early Option Exercise? Working paper, University of Florida, 2012.
   Google Scholar
• F. Angelini and S. Herzel, Delta hedging in discrete time under stochastic interest rate, J. Comput. Appl. Math. 259 (2014), pp. 385–393. doi: 10.1016/j.cam.2013.06.022
   Web of Science ®Google Scholar
• T. Arai and Y. Imai, On the difference between locally risk-minimizing and delta hedging strategies for exponential Lévy models, Jpn. J. Indust. Appl. Math. 34 (2017), pp. 845–858. doi: 10.1007/s13160-017-0268-6
   Web of Science ®Google Scholar
• G. Bakshi, C. Cao, and Z. Chen, Pricing and hedging long-term options, J. Econometrics 94 (2000), pp. 277–318. doi: 10.1016/S0304-4076(99)00023-8
   Web of Science ®Google Scholar
• G. Bakshi, C. Cao, and Z. Chen, Option pricing and hedging performance under stochastic volatility and stochastic interest rates, in Handbook of Quantitative Finance and Risk Management, C.F. Lee, A.C. Lee, and J. Lee, eds., Springer, Boston, MA, 2010, pp. 547–574.
   Google Scholar
• L.V. Ballestra and G. Pacelli, Pricing European and American options with two stochastic factors: A highly efficient radial basis function approach, J. Econom. Dynam. Control 37 (2013), pp. 1142–1167. doi: 10.1016/j.jedc.2013.01.013
   Web of Science ®Google Scholar
• L.V. Ballestra and C. Sgarra, The evaluation of American options in a stochastic volatility model with jumps: An efficient finite element approach, Comput. Math. Appl. 60 (2010), pp. 1571–1590. doi: 10.1016/j.camwa.2010.06.040
   Web of Science ®Google Scholar
• N. Beliaeva and S. Nawalkha, A simple approach to pricing American options under the Heston stochastic volatility model, J. Deriv. 17 (2010), pp. 25–43. doi: 10.3905/jod.2010.17.4.025
   Web of Science ®Google Scholar
• F. Black and M. Scholes, The pricing of options and corporate liabilities, J. Polit. Econ. 81 (1973), pp. 637–654. doi: 10.1086/260062
   Web of Science ®Google Scholar
• D. Brigo and F. Mercurio, Interest Rate Models-Theory and Practice: With Smile, Inflation and Credit, 2nd ed., Springer Finance, Springer, New York, NY, USA, 2006.
   Google Scholar
• O. Burkovska, B. Haasdonk, J. Salomon, and B. Wohlmuth, Reduced basis methods for pricing options with the Black–Scholes and Heston model, SIAM J. Financ. Math. 6 (2014), pp. 685–712. doi: 10.1137/140981216
   Google Scholar
• P. Carr and L. Wu, The finite moment log stable process and option pricing, J. Finance 58 (2003), pp. 753–777. doi: 10.1111/1540-6261.00544
   Web of Science ®Google Scholar
• C. Chiarella and A. Ziogas, Pricing American Options under Stochastic Volatility, Working paper, University of Technology, Sydney, 2006.
   Google Scholar
• P. Christoffersen, S.L. Heston, and K. Jacobs, The shape and term structure of the index option smirk: Why multifactor stochastic volatility models work so well, Manage. Sci. 55 (2009), pp. 1914–1932. doi: 10.1287/mnsc.1090.1065
   Web of Science ®Google Scholar
• 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
   Web of Science ®Google Scholar
• W. Feller, Two singular diffusion problems, Ann. Math. 54(2) (1951), pp. 173–182. doi: 10.2307/1969318
   Google Scholar
• J.-P. Fouque, G. Papanicolaou, and R. Sircar, From the implied volatility skew to a robust correction to Black–Scholes American option prices, Int. J. Theor. Appl. Finance 4 (2001), pp. 651–675. doi: 10.1142/S0219024901001139
   Google Scholar
• L.A. Grzelak, C.W. Oosterlee, and S.V. Weeren, Extension of stochastic volatility equity models with the Hull–White interest rate process, Quant. Finance 12 (2012), pp. 89–105. doi: 10.1080/14697680903170809
   Web of Science ®Google Scholar
• S. Herzel, Evaluating discrete dynamic strategies in affine models, Quant. Finance 15 (2015), pp. 313–326. doi: 10.1080/14697688.2011.637075
   Web of Science ®Google Scholar
• 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
   Web of Science ®Google Scholar
• S. Ikonen and J. Toivanen, Componentwise splitting methods for pricing American options under stochastic volatility, Int. J. Theor. Appl. Finance 10 (2007), pp. 331–361. doi: 10.1142/S0219024907004202
   Google Scholar
• S. Ikonen and J. Toivanen, Efficient numerical methods for pricing American options under stochastic volatility, Numer. Methods Partial Differ. Equations 24 (2008), pp. 104–126. doi: 10.1002/num.20239
   Web of Science ®Google Scholar
• 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
   Web of Science ®Google Scholar
• K. Ito and J. Toivanen, Lagrange multiplier approach with optimized finite difference stencils for pricing American options under stochastic volatility, SIAM J. Sci. Comput. 31 (2009), pp. 2646–2664. doi: 10.1137/07070574X
   Web of Science ®Google Scholar
• A. Kunoth, C. Schneider, and K. Wiechers, Multiscale methods for the valuation of American options with stochastic volatility, Int. J. Comput. Math. 89 (2012), pp. 1145–1163. doi: 10.1080/00207160.2012.672732
   Web of Science ®Google Scholar
• A. Kurpiel and T. Roncalli, Option Hedging with Stochastic Volatility, Working paper, City University Business School, 1998.
   Google Scholar
• F.A. Longstaff and E.S. Schwartz, Valuing American options by simulation: A simple least-squares approach, Rev. Financ. Stud. 14 (2001), pp. 113–147. doi: 10.1093/rfs/14.1.113
   Web of Science ®Google Scholar
• A. Medvedev and O. Scaillet, Approximation and calibration of short-term implied volatilities under jump-diffusion stochastic volatility, Rev. Financ. Stud. 20 (2007), pp. 427–459. doi: 10.1093/rfs/hhl013
   Web of Science ®Google Scholar
• A. Medvedev and O. Scaillet, Pricing American options under stochastic volatility and stochastic interest rates, J. Financ. Econ. 98 (2010), pp. 145–159. doi: 10.1016/j.jfineco.2010.03.017
   Web of Science ®Google Scholar
• N. Rambeerich, D.Y. Tangman, M.R. Lollchund, and M. Bhuruth, High-order computational methods for option valuation under multifactor models, Eur. J. Oper. Res. 224 (2013), pp. 219–226. doi: 10.1016/j.ejor.2012.07.023
   Web of Science ®Google Scholar
• B.R. Rambharat and A.E. Brockwell, Sequential Monte Carlo pricing of American-style options under stochastic volatility model, Ann. Appl. Stat. 4 (2010), pp. 222–265. doi: 10.1214/09-AOAS286
   Web of Science ®Google Scholar
• P. Ruckdeschel, T. Sayer, and A. Szimayer, Pricing American options in the Heston model: A close look at incorporating correlation, J. Deriv. 20 (2013), pp. 9–29. doi: 10.3905/jod.2013.20.3.009
   Web of Science ®Google Scholar
• A. Sepp, An approximate distribution of delta-hedging errors in a jump-diffusion model with discrete trading and transaction costs, Quant. Finance 12 (2012), pp. 1119–1141. doi: 10.1080/14697688.2010.494613
   Web of Science ®Google Scholar
• Y. Sun, Efficient pricing and hedging under the double Heston stochastic volatility jump-diffusion model, Int. J. Comput. Math. 92 (2015), pp. 2551–2574. doi: 10.1080/00207160.2015.1079311
   Web of Science ®Google Scholar
• M. Vellekoop and H. Nieuwenhuis, A tree-based method to price American options in the Heston model, J. Comput. Finance 13 (2009), pp. 1–21. doi: 10.21314/JCF.2009.197
   Web of Science ®Google Scholar
• S. Zhang and J. Zhao, Efficient simulation for pricing barrier options with two-factor stochastic volatility and stochastic interest rate, Math. Probl. Eng. 2017 (2017), pp. 1–8.
   Google Scholar
• J. Zhu, A Simple and Exact Simulation Approach to Heston Model, Working paper, 2008. Available at SSRN: https://ssrn.com/abstract=1153950.
   Google Scholar