Abstract
We introduce a formal test to detect whether a times series of financial log-returns is consistent with the Heston stochastic volatility model as data generating process. The test is based on the auto-covariance structure of the integrated volatility, which is available in closed form for the model under investigation. The test suggested in this contribution also relies on the outcomes of a companion paper where we prove asymptotic results for the distribution of sample moments of the squared log-returns in the fully-specified Heston model.
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References
Andersen, L.B.G.: Simple and efficient simulation of the Heston stochastic volatility model. J. Comput. Finance 11(3), 1–42 (2008)
Black, F., Scholes, M.: The pricing of options and corporate liabilities. J. Polit. Econ. 81, 637–659 (1973)
Cont, R.: Empirical properties of asset returns: stylized facts and statistical issues. Quant. Finance 1(2), 223–236 (2001)
Ewald, C.O., Zhang, A.: A new method for the calibration of stochastic volatility models: the Malliavin gradient method. Quant. Finance 6(2), 147–158 (2006)
Figà-Talamanca, G.: Limit results for stochastic volatility models. Quaderni del Dipartimento di Economia, Finanza e Statistica 63 (2008)
Figà-Talamanca, G.: Testing volatility autocorrealtion in the CEV model. Comput. Stat. Data Anal. 53, 2201–2218 (2009)
Heston, S.L.: A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Financ. Stud. 6, 327–343 (1993)
Hull, J., White, A.: The pricing of options on assets with stochastic volatility. J. Finance 42(2), 281–300 (1987)
Lehmann, E.L.: Elements of Large-Sample Theory. Springer, Berlin (1998)
Sepp, A.: Pricing options on realized variance in the Heston model with jumps in returns and volatility. J. Comput. Finance 11(4), 33–70 (2008)
Stein, E., Stein, J.: Stock price distributions with stochastic volatility. Rev. Financ. Stud. 4, 27–752 (1991)
Wiggins, J.: Option values under stochastic volatilities. J. Financ. Econ. 19(351), 372 (1987)
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Figà-Talamanca, G. (2014). A Statistical Test for the Heston Model. In: Perna, C., Sibillo, M. (eds) Mathematical and Statistical Methods for Actuarial Sciences and Finance. Springer, Cham. https://doi.org/10.1007/978-3-319-05014-0_24
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DOI: https://doi.org/10.1007/978-3-319-05014-0_24
Publisher Name: Springer, Cham
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