Abstract
In this paper, we present American option pricing under Heston–Hull–White’s stochastic volatility and stochastic interest rate model. To do this, we first discretize the stochastic processes with Euler discretization scheme. Then, we price American option by using least-squares Monte Carlo algorithm. We also compare the numerical results of our model with the Heston-CIR model. Finally, numerical results show the efficiency of the proposed algorithm for pricing American option under the Heston–Hull–White model.
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AitSahlia, F., Goswami, M., & Guha, S. (2008). American option pricing under stochastic volatility: An empirical evaluation. Journal of Computational Management Science, 7, 789-206.
Barraquand, J., & Martineau, D. (1995). Numerical valuation of high dimensional multivariate American securities. Journal of Financial and Quantitative Analysis, 30, 383–405.
Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637–654.
Boyarchenko, S. I., & LevendorskiĬ, S. Z. (2013). American options in the Heston model with stochastic interest rate and its generalizations. Journal of Applied Mathematical Finance, 20, 26–49.
Broadie, M., & Glasserman, P. (1997a). Monte Carlo methods for pricing high-dimensional American options: An overview, working paper. New York: Columbia University.
Broadie, M., & Glasserman, P. (1997b). Pricing American-style securities using simulation. Journal of Economic Dynamics and Control, 21, 1323–1352.
Broadie, M., Glasserman, P., & Jain, G. (1997). Enhanced Monte Carlo estimates for American option prices. The Journal of Derivatives, 5, 25–44.
Chiarella, C., & Ziogas, A. (2005). Pricing American options under stochastic volatility. Computing in Economics and Finance, 77. Society for Computational Economics.
Cox, J. C., Ingersoll, J. E., & Ross, S. A. (1985). A theory of the term structure of interest rates. Econometrica, 53, 385–408.
Creal, D. (2012). A survey of sequential Monte Carlo methods for economics and finance. Econometric Reviews, 31, 245–296.
Gauthier, P., & Possamai, D. (2011). Efficient simulation of the double Heston model. IUP Journal of Computational Mathematics, 4(3), 23–73.
Glasserman, P. (2003). Monte Carlo methods in financial engineering (1st ed.). New York: Springer.
Grzelak, L. A., Oosterlee, C. W., & Weeren, S. V. (2012). Extension of stochastic volatility equity models with Hull-White interest rate process. Quantitative Finance, 12, 89–105.
Heston, S. L. (1993). A closed-form solution for options with stochastic volatility with applications to bonds and currency options. The Review of Financial Studies, 6(2), 327–343.
in’t Hout, K., Bierkens, J., van der Ploeg, A. P. C., & in’t Panhuis, J. (2007a). A semi-closed form analytic pricing formula for call options in a hybrid Heston–Hull–White model. In Proceedings of the 58th study group mathematics with industry (pp. 101–105).
in’t Hout, K., Bierkens, J., van der Ploeg, A. P. C., & in’t Panhuis, J. (2007b). A semi-closed form analytic pricing formula for call options in a hybrid Heston–Hull–White model. In Proceedings of the 58th study group mathematics with industry (pp. 101–105).
Jia, Q. (2009). Pricing American options using Monte Carlo methods. Uppsala: Department of Mathematics, Uppsala University.
Kammeyer, H., & Kienitz, J. (2012b). The Heston Hull White model II: Fourier transform and Monte Carlo simulation. Wilmott Journal.
Kienitz, J., & Wetterau, D. (2012). Financial modelling: Theory, implementation and practice with MATLAB source (1st ed.). New York: Wiley.
Longstaff, F. A., & Schwartz, E. S. (2001). Valuing American options by simulation: A simple least-squares approach. Review of Financial Studies, 14(1), 113–147.
Raymar, S., & Zwecher, M. (1997). A Monte Carlo valuation of American call options on the maximum of several stocks. Journal of Derivatives, 5, 7–23.
Scott, L. (1987). Option pricing when the variance changes randomly: Theory, estimation, and an application. The Journal of Financial and Quantitative Analysis, 22, 419–438.
Stein, E., & Stein, J. (1991). Stock price distributions with stochastic volatility: An analytic approach. The Review of Financial Studies, 4, 727–752.
Tilley, J. A. (1993). Valuing American options in a path simulation model. Transactions of the Society of Actuaries, 45, 83–104.
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Samimi, O., Mardani, Z., Sharafpour, S. et al. LSM Algorithm for Pricing American Option Under Heston–Hull–White’s Stochastic Volatility Model. Comput Econ 50, 173–187 (2017). https://doi.org/10.1007/s10614-016-9598-8
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DOI: https://doi.org/10.1007/s10614-016-9598-8