Abstract
The bias between the expected realized variance under the historical measure and the risk neutral probability introduces the concept of the variance risk premium (VRP). Our work introduced a probabilistic modeling of the VRP via a parametric class of stochastic volatility models which incorporates the nonlinear class.
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References
Alòs, E., Ewald, C.-O.: Malliavin differentiability of the Heston volatility and applications to option pricing. Available at SSRN 986316 (2007)
Carr, P., Sun, J.: A new approach for option pricing under stochastic volatility. Rev. Deriv. Res. 10, 87–150 (2007)
Carr, P., Wu, L.: Variance risk premiums. Rev. Financ. Studies 22, 1311–1341 (2009)
Chorro, C., Guégan, D., Ielpo, F.: A Time Series Approach to Option Pricing. Springer, Berlin (2014)
Demeterfi, K., Derman, E., Kamal, M., Zou, J.: A guide to volatility and variance swaps. J. Deriv. 6, 9–32 (1999)
Di Nunno, G., Øksendal, B., Proske, F.: Malliavin Calculus for Lévy Processes with Applications to Finance. Springer, Berlin (2009)
Diop, A.: Sur la discrétisation et le comportement a petit bruit d’eds unidimensionnelles dont les coefficients sont a dérivées singulieres, These Université de Nice Sophia-Antipolis (2003)
Engle, R.F.: Autoregressive conditional heteroscedasticity with estimates of the variance of united kingdom inflation. Econometrica: J. Econ. Soc. 50(4), 987–1007 (1982)
Harrison, J.M., Kreps, D.M.: Martingales and arbitrage in multiperiod securities markets. J. Econ. Theory 20, 381–408 (1979)
Heston, S.L.: A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Financ. Studies 6, 327–343 (1993)
Lamberton, D., Lapeyre, B.: Introduction to Stochastic Calculus Applied to Finance. CRC Press, Boca Raton (2007)
Nelson, D.B.: Conditional heteroskedasticity in asset returns: a new approach. Econometrica: J. Econ. Soc. 59(2), 347–370 (1991)
Nualart, D.: The Malliavin Calculus and Related Topics, vol. 1995. Springer, Berlin (2006)
Ocone, D.: Malliavin’s calculus and stochastic integral representations of functional of diffusion processes. Stochastics: Int. J. Prob. Stoch. Processes 12, 161–185 (1984)
Acknowledgements
This research received funding from the European Union Seventh Framework Programme (FP7/2007–2013) under grant agreement No. 289032 (HPCFinance).
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Gnameho, K., Kanniainen, J., Yue, Y. (2017). Modeling Variance Risk Premium. In: Corazza, M., Legros, F., Perna, C., Sibillo, M. (eds) Mathematical and Statistical Methods for Actuarial Sciences and Finance . Springer, Cham. https://doi.org/10.1007/978-3-319-50234-2_11
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DOI: https://doi.org/10.1007/978-3-319-50234-2_11
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