Abstract
Over the past few years, model complexity in quantitative finance has increased substantially in response to earlier approaches that did not capture critical features for risk management. However, given the preponderance of the classical Black–Scholes model, it is still not clear that this increased complexity is matched by additional accuracy in the ultimate result. In particular, the last decade has witnessed a flurry of activity in modeling asset volatility, and studies evaluating different alternatives for option pricing have focused on European-style exercise. In this paper, we extend these empirical evaluations to American options, as their additional opportunity for early exercise may incorporate stochastic volatility in the pricing differently. Specifically, the present work compares the empirical pricing and hedging performance of the commonly adopted stochastic volatility model of Heston (Rev Financial Stud 6:327–343, 1993) against the traditional constant volatility benchmark of Black and Scholes (J Polit Econ 81:637–659, 1973). Using S&P 100 index options data, our study indicates that this particular stochastic volatility model offers enhancements in line with their European-style counterparts for in-the-money options. However, the most striking improvements are for out-of-the-money options, which because of early exercise are more valuable than their European-style counterparts, especially when volatility is stochastic.
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References
Amin K, Jarrow R (1992) Option pricing on a risky asset in a stochastic interest economy. Math Finance 2: 881–910
Amin K, Ng V (1993) Option valuation with system stochastic volatility. J Finance 48: 881–910
Bailey W, Stulz R (1989) The pricing of stock index options in a general equilibrium model. J Financ Quant Anal 24: 1–12
Bakshi G, Cao C, Chen Z (1997) Empirical performance of alternative option pricing models. J Finance 52: 2003–2049
Bates D (1996) Jumps and stochastic volatility: exchange rate processes implicit in deutschemark options. Rev Financ Stud 9: 69–108
Black F (1976) Studies of stock price volatility changes. In: Proceedings of the 1976 meetings of the American Statistical Association, pp 171–181
Black F, Scholes M (1973) The pricing of options and corporate liabilities. J Polit Econ 81: 637–659
Carrière J (1996) Valuation of the early-exercise price for derivatives using simulations and splines. Insurance Math Econ 19: 19–30
Cont R, Tankov P (2000) Financial modelling with jump processes, 1st edn. Chapman and Hall/CRC Press, Boca Raton
Engle R, Lee G (1996) Estimating diffusion models of stochastic volatility. Modeling stock market volatility. Academic Press, Inc, New York, pp 333–355
Feller W (1951) Two singular diffusion problems. Ann Math 54: 173–182
Fouque J, Papanicolaou G, Sircar R (2000) Derivatives in finacial markets with stochastic volatility. Cambridge University Press, Cambridge
Glasserman P (2004) Monte carlo methods in financial engineering, 1st edn. Springer, Heidelberg
Gourieroux C, Monfort A, Renault E (1993) Indirect inference. J Appl Economet 8: s85–s118
Heston S (1993) A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev Financ Stud 6: 327–343
Hull JC, White A (1987) The pricing of options on assets with stochastic volatilities. J Finance 42: 281–300
Ikonen S, Toivanen J (2007) Efficient numerical methods for pricing american options under stochastic volatility. Numer Methods Partial Differ Equat 24(1): 104–126
Longstaff FA, Schwartz ES (2001) Valuing american options by simulation: a simple least-squares approach. Rev Financ Stud 14: 113–147
Luenberger D (1998) Investment science. Oxford University Press, Oxford
Melino A, Turnbull S (1990) Pricing foreign currency options with stochastic volatility. J Economet 45: 239–265
Melino A, Turnbull S (1995) Misspecification and the pricing and hedging of long-term foreign currency options. Int Money Finance 14: 373–393
Nelson D (1990) Arch models as diffusion approximations. J Economet 45: 7–38
Newey W, West K (1987) A simple positive definite heteroscedasticity and autocorrelation consistent covariance matrix. Econometrica 55: 703–708
Rossi P (1996) Modeling stock market volatility. Academic Press, New York
Scott L (1987) Option pricing when the variance changes randomly: theory, estimators, and applications. J Financ Quant Anal 22: 419–438
Scott L (1997) Pricing stock options in a jump-diffusion model with stochastic volatility and interest rates: an application of fourier inversion methods. Math Finance 7: 413–426
Stein E, Stein J (1991) Stock price distributions with stochastic volatility. Rev Financ Stud 4: 727–752
Zhang J, Shu J (2003) Pricing S&P 500 index options with heston’s model. In: IEEE Computational intelligence for financial engineering proceedings, pp 85–92
Zvan R, Forsyth PA, Vetzal KR (1998) Penalty methods for american options with stochastic volatility. J Comput Appl Math 91: 199–218
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AitSahlia, F., Goswami, M. & Guha, S. American option pricing under stochastic volatility: an empirical evaluation. Comput Manag Sci 7, 189–206 (2010). https://doi.org/10.1007/s10287-008-0083-2
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DOI: https://doi.org/10.1007/s10287-008-0083-2