References
- C. Ball and A. Roma, Stochastic volatility option pricing, J. Financ. Quant. Anal. 29(4) (1994), pp. 589–607. doi: 10.2307/2331111
- D. Bates, Jump and stochastic volatility: Exchange rate processes implicit in Deutsche mark in options, Rev. Financ. Stud. 9(1) (1996), pp. 69–107. doi: 10.1093/rfs/9.1.69
- M. Broadie and A. Jain, Pricing and heding volatility derivatives, J. Derivatives. 15(3) (2008), pp. 7–24. doi: 10.3905/jod.2008.702503
- M. Broadie and O. Kaya, Exact simulation of option Greeks under stochastic volatility and jump diffusion models, Proceedings of the 2004 Winter Simulation Conference, Washington, 1607–1615, 2004.
- M. Broadie and O. Kaya, Exact simulation of stochastic volatility and other affine jump diffusion processes, Oper. Res. 54(2) (2006), pp. 217–231. doi: 10.1287/opre.1050.0247
- O. Brockhaus and D. Long, Volatility swap made simple, Risk. 2(1) (2000), pp. 92–96.
- P. Carr and R. Lee, Robust replication of volatility derivatives, Working paper, Courant Institute and University of Chicago, 2005. Available at http://math.nyu.edu/research/carrp/research.html
- J. Carr, P. Geman, H. Madan, and D. Yor, Pricing options on realized variance, Financ. Stochastic 9 (2005), pp. 453–475. doi: 10.1007/s00780-005-0155-x
- Z.Y. Chen and P. Glasserman, Fast pricing of basket default swaps, Oper. Res. 56(2) (2008), pp. 286–303. doi: 10.1287/opre.1070.0456
- E. Derman, M. Kamal, J. Zou, and K. Demeterfi, A guide to volatility and variance swaps, J. Derivatives 6(4) (1999), pp. 9–32. doi: 10.3905/jod.1999.319129
- J. Detemple and C. Osakwe, The valuation of volatility options, Eur. Financ. Rev. 4(1) (2000), pp. 21–50. doi: 10.1023/A:1009814324980
- F. D'Ippoliti, E. Moretto, S. Pasquali, and B. Trivellato, Exact pricing with stochastic volatility and jumps, Int. J. Theor. Appl. Financ. 13(6) (2010), pp. 901–929. doi: 10.1142/S0219024910006042
- M. Fu, D. Madan, and T. Wang, Pricing continuous time Asian options: a comparison of Monte Carlo and Laplace transform inversion methods, J. Comput. Financ. 2(2) (1999), pp. 49–74.
- P. Glasserman, Monte Carlo Methods in Financial Engineering, Springer, New York, 2004.
- P. Glasserman and J.Y. Li, Importance sampling for portfolio credit risk, Manage. Sci. 51(11) (2005), pp. 1643–1656. doi: 10.1287/mnsc.1050.0415
- C.H. Han and Y. Lai, A smooth estimator for MC/QMC methods in finance, Math. Comput. Simul. 81(3) (2010), pp. 536–550. doi: 10.1016/j.matcom.2010.07.013
- S.L. Heston, A closed-form solution for options with stochastic volatility with applications to bond and currency options, Rev. Financ. Stud. 6(2) (1993), pp. 327–343. doi: 10.1093/rfs/6.2.327
- S. Heston and S. Nandi, Derivatives on volatility: some simple solutions based on observables, Federal Reserve Bank of Atlanta, Working paper, 2000.
- J. Hull and A. White, The use of the control variate technique in option pricing, J. Financ. Quant. Anal. 23(3) (1987), pp. 237–251. doi: 10.2307/2331065
- J. Hull and A. White, The pricing of options on assets with stochastic volatilities, J. Financ. 42(2) (1987), pp. 281–300. doi: 10.1111/j.1540-6261.1987.tb02568.x
- R.A. Jarrow and E.R. Rosenfeld, Jump risks and the intertemporal capital asset pricing model, J. Bus. 57(3) (1984), pp. 337–351. doi: 10.1086/296267
- A. Javaheri, P. Wilmott, and G. Haug, GARCH and volatility swaps, Quant. Financ. 4(5) (2004), pp. 589–595. doi: 10.1080/14697680400000040
- L.S. Jiang, C.L. Xu, X.M. Ren, and S.H. Li, Mathematical Models and Cases Analysis for Financial Derivatives, in Chinese, Tianfu Zhao ed., High Education Press, Beijing, 2008, pp. 29–32.
- M.S. Joshi and D. Kainth, Rapid and accurate development of prices and Greeks for nth to default credit swaps in the Li model, Res. Pap. 4(3) (2004), pp. 266–275.
- M.S. Joshi and T. Leung, Using Monte Carlo simulation and importance sampling to rapidly obtain jump-diffusion prices of continuous barrier options, J. Comput. Financ. 10(4) (2007), pp. 93–105.
- A.G. Kemna and A.C. Vorst, A pricing method for options based on average asset values, J. Bank. Financ. 14(1) (1990), pp. 113–129. doi: 10.1016/0378-4266(90)90039-5
- S.G. Kou, A jump diffusion model for option pricing, Manage. Sci. 48(8) (2002), pp. 1086–1101. doi: 10.1287/mnsc.48.8.1086.166
- T. Little and V. Pant, A finite difference method for the valuation of variance swaps, J. Comput. Financ. 5(Fall) (2001), pp. 81–103.
- J. Ma and C. Xu, An efficient control variate method for pricing variance derivatives, J. Comput. Appl. Math. 235(1) (2010), pp. 108–119. doi: 10.1016/j.cam.2010.05.017
- S.J. Malene and S. Mikkel, Efficient control variates and strategies for Bermudan swaptions in a Libor market model, J. Derivatives 12(4) (2005), pp. 20–33. doi: 10.3905/jod.2005.517183
- A. Quarteroni, R. Sacco, and F. Saleri, Numerical Mathematics, Science Press, Beijing, 2006.
- L.O. Scott, Option pricing when the variance changes randomly: Theory, estimation, and an application, J. Financ. Quant. Anal. 22(4) (1987), pp. 419–438. doi: 10.2307/2330793
- L. Scott, Pricing stock options in a jump-diffusion model with stochastic volatility and interest rates: Applications of fourier inversion methods, Math. Financ. 7(4) (1997), pp. 413–426. doi: 10.1111/1467-9965.00039
- E.M. Stein, and J.C. Stein, Stock price distributions with stochastic volatility: An analytic approach, Rev. Financ. Stud. 4(4) (1991), pp. 727–752. doi: 10.1093/rfs/4.4.727
- Y. Su and M.C. Fu, Importance sampling in derivative securities pricing, Proceedings of the 2000 Winter Simulation Conference, Orlando, 587–596, 2000.
- G. Yan and F.B. Hanson, Option pricing for a stochastic-volatility jump-diffusion model with log-uniform jump-amplitudes, Proceedings of American Control Conference, Minneapolis, 2989–2994, 2006.