An efficient conditional Monte Carlo method for European option pricing with stochastic volatility and stochastic interest rate

References

• M. Abudy and Y. Izhakian, Pricing stock options with stochastic interest rate, Int. J. Portfolio Anal. Manag. 1 (2013), pp. 250–277. doi: 10.1504/IJPAM.2013.054408
   Google Scholar
• L.B.G. Andersen, Efficient simulation of the Heston stochastic volatility model, J. Comput. Finan. 11 (2008), pp. 1–42. doi: 10.21314/JCF.2008.189
   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
• N. Bolia, S. Juneja, and P. Glasserman, Function-approximation-based importance sampling for pricing American options, in Proceedings of the 36th Conference on Winter Simulation. Winter Simulation Conference, WSC' 04, 2004, pp. 604–611. Available at http://dl.acm.org/citation.cfm?id=1161734.1161846.
   Google Scholar
• P.P. Boyle, Options: a Monte Carlo approach, J. Financ. Econ. 4 (1977), pp. 323–338. doi: 10.1016/0304-405X(77)90005-8
   Web of Science ®Google Scholar
• P. Boyle, M. Broadie, and P. Glasserman, Monte Carlo methods for security pricing, J. Econom. Dynam. Control 21 (1997), pp. 1267–1321. doi: 10.1016/S0165-1889(97)00028-6
   Web of Science ®Google Scholar
• M. Broadie and Ö Kaya, Exact simulation of stochastic volatility and other affine jump diffusion processes, Oper. Res. 54 (2006), pp. 217–231. doi: 10.1287/opre.1050.0247
   Web of Science ®Google Scholar
• P. Carr and D.B. Madan, Option valuation using the fast Fourier transform, J. Comput. Financ. 2 (1999), pp. 61–73. doi: 10.21314/JCF.1999.043
   Google Scholar
• 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
   Web of Science ®Google Scholar
• D.M. Dang, K.R. Jackson, and M. Mohammadi, Dimension and variance reduction for Monte Carlo methods for high-dimensional models in finance, Appl. Math. Finance 22 (2015), pp. 522–552. doi: 10.1080/1350486X.2015.1110492
   Google Scholar
• D.M. Dang, K.R. Jackson, and S. Sues, A dimension and variance reduction Monte-Carlo method for option pricing under jump-diffusion models, Appl. Math. Finance.
   Google Scholar
• K.D. Dingeç and W. Hörmann, Control variates and conditional Monte Carlo for basket and Asian options, Insur. Math. Econom. 52 (2013), pp. 421–434. doi: 10.1016/j.insmatheco.2013.03.002
   Web of Science ®Google Scholar
• J.P. Fouque and T.A. Tullie, Variance reduction for Monte Carlo simulation in a stochastic volatility environment, Quant. Finance 2 (2002), pp. 24–30. doi: 10.1088/1469-7688/2/1/302
   Google Scholar
• P. Glasserman, Monte Carlo Methods in Financial Engineering, Springer, New York, 2004.
   Google Scholar
• L.A. Grzelak and C.W. Oosterlee, On cross-currency models with stochastic volatility and correlated interest rates, Appl. Math. Finance 19 (2012), pp. 1–35. doi: 10.1080/1350486X.2011.570492
   Google Scholar
• L.A. Grzelak and C.W. Oosterlee, On the Heston model with stochastic interest rates, SIAM J. Finan. Math. 2 (2012), pp. 255–286. doi: 10.1137/090756119
   Google Scholar
• L.A. Grzelak, C.W. Oosterlee, and S.V. Weeren, The affine Heston model with correlated gaussian interest rates for pricing hybrid derivatives, Quant. Finance 11 (2011), pp. 1647–1663. doi: 10.1080/14697688.2011.615216
   Web of Science ®Google Scholar
• X.J. He and S.P. Zhu, A closed-form pricing formula for European options under the Heston model with stochastic interest rate, J. Comput. Appl. Math. 335 (2018), pp. 323–333. doi: 10.1016/j.cam.2017.12.011
   Web of Science ®Google Scholar
• D. Heath, R. Jarrow, and A. Morton, Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation, Econometrica 60 (1992), pp. 77–105. doi: 10.2307/2951677
   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. Finan. Stud. 6 (1993), pp. 327–343. doi: 10.1093/rfs/6.2.327
   Web of Science ®Google Scholar
• J. Hull and A. White, The pricing of options on assets with stochastic volatilities, J. Finance 42 (1987), pp. 281–300. doi: 10.1111/j.1540-6261.1987.tb02568.x
   Web of Science ®Google Scholar
• J. Hull and A. White, Pricing interest-rate-derivative securities, Rev. Finan. Stud. 3 (1990), pp. 573–592. doi: 10.1093/rfs/3.4.573
   Web of Science ®Google Scholar
• A.G.Z. Kemna and A.C.F. Vorst, A pricing method for options based on average asset values, J. Banking Finan. 14 (2004), pp. 113–129. doi: 10.1016/0378-4266(90)90039-5
   Google Scholar
• Y. Liang and C. Xu, Efficient accelerating method of conditional Monte-Carlo simulation for two-factor option pricing model, J. Tongji Univ. 42 (2014), pp. 645–650.
   Google Scholar
• R. Lord, R. Koekkoek, and D.V. Dijk, A comparison of biased simulation schemes for stochastic volatility models, Quant. Finance 10 (2010), pp. 177–194. doi: 10.1080/14697680802392496
   Web of Science ®Google Scholar
• J.M. Ma and C. Xu, An efficient control variate method for pricing variance derivatives, J. Comput. Appl. Math. 235 (2010), pp. 108–119. doi: 10.1016/j.cam.2010.05.017
   Web of Science ®Google Scholar
• R.C. Merton, Theory of rational option pricing, Bell J. Econ. Manag. Sci. 4 (1973), pp. 141–183. doi: 10.2307/3003143
   Google Scholar
• J. Pan, The jump-risk premia implicit in options: evidence from an integrated time-series study, J. Financ. Econ. 63 (2002), pp. 3–50. doi: 10.1016/S0304-405X(01)00088-5
   Web of Science ®Google Scholar
• S. Ross, A First Course in Probability. 9th ed. Pearson, Boston, 2014.
   Google Scholar
• L.O. Scott, Option pricing when the variance changes randomly: Theory, estimation, and an application, J. Financ. Quant. Anal. 22 (1987), pp. 419–438. doi: 10.2307/2330793
   Web of Science ®Google Scholar
• L.O. Scott, Pricing stock options in a jump-diffusion model with stochastic volatility and interest rates: Applications of Fourier inversion methods, Math. Financ. 7 (2010), pp. 413–426. doi: 10.1111/1467-9965.00039
   Google Scholar
• E.M. Stein and J.C. Stein, Stock price distributions with stochastic volatility: An analytic approach, Rev. Financ. Stud. 4 (1991), pp. 727–752. doi: 10.1093/rfs/4.4.727
   Web of Science ®Google Scholar
• Y. Sun and C. Xu, A hybrid Monte Carlo acceleration method of pricing basket options based on splitting, J. Comput. Appl. Math. 342 (2018), pp. 292–304. doi: 10.1016/j.cam.2018.03.045
   Web of Science ®Google Scholar
• O. Vasicek, An equilibrium characterization of the term structure, J. Financ. Econom. 5 (1977), pp. 177–188. doi: 10.1016/0304-405X(77)90016-2
   Web of Science ®Google Scholar
• G.A. Willard, Calculating prices and sensitivities for path-independent derivative securities in multifactor models, J. Derivatives 5 (1997), pp. 45–61. doi: 10.3905/jod.1997.407982
   Google Scholar