Dell'Era, Mario
(2010):
*Vanilla Option Pricing on Stochastic Volatility market models.*
Forthcoming in: Quantitative Finance

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## Abstract

We want to discuss the option pricing on stochastic volatility market models, in which we are going to consider a generic function β (νt ) for the drift of volatility process. It is our intention choose any equivalent martingale measure, so that the drift of volatility process, respect at the new measure, is zero. This technique is possible when the Girsanov theorem is satisﬁed, since the stochastic volatility models are uncomplete markets, thus one has to choice an arbitrary risk price of volatility. In all this cases we are able to compute the price of Vanilla options in a closed form. To name a few, we can think to the popular Heston’s model, in which the solution is known in literature, unless of an inverse Fourier transform.

Item Type: | MPRA Paper |
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Original Title: | Vanilla Option Pricing on Stochastic Volatility market models |

English Title: | Vanilla Option Pricing on Stochastic Volatility market models |

Language: | English |

Keywords: | Vanilla Option pricing on Stochastic volatility market models |

Subjects: | G - Financial Economics > G1 - General Financial Markets C - Mathematical and Quantitative Methods > C0 - General |

Item ID: | 25645 |

Depositing User: | Mario Dell'Era |

Date Deposited: | 05 Oct 2010 00:08 |

Last Modified: | 28 Sep 2019 04:30 |

References: | Andersen, L,. and J. Andreasen (2002), Volatile Volatilities, Risk Magazine, December. Andersen, L. and R. Brotherton-Ratcliffe (2005), Extended LIBOR market models with stochastic volatility, Journal of Computational Finance, vol. 9, no.1, pp. 1-40. Andersen, L. and V. Piterbarg (2005), “Moment explosions in stochastic volatility models, Finance and Stochastics, forthcoming. Andreasen, J. (2006), Long-dated FX hybrids with stochastic volatility,Working paper, Bank of America. Broadie, M. and O¨ . Kaya (2006), Exact simulation of stochastic volatility and other affine jump diffusion processes, Operations Research, vol. 54, no. 2. Broadie, M. and O¨ . Kaya (2004), Exact simulation of option greeks under stochastic volatility and jump diffusion models,” in R.G. Ingalls, M.D. Rossetti, J.S. Smith and B.A. Peters (eds.), Proceedings of the 2004 Winter Simulation Conference. Carr, P. and D. Madan (1999), Option Pricing and the fast Fourier transform, Journal of Computational Finance, 2(4), pp. 61-73. Cox, J., J. Ingersoll and S.A. Ross (1985), A theory of the term structure of interest rates, Econometrica, vol. 53, no. 2, pp. 385-407. Duffie, D. and P. Glynn (1995), Efficient Monte Carlo simulation of security prices, Annals of Applied Probability, 5, pp. 897-905 Duffie, D., J. Pan and K. Singleton (2000), Transform analysis and asset pricing for affine jump diffusions, Econometrica, vol. 68, pp. 1343-1376. Dufresne, D. (2001), The integrated square-root process, Working paper, University of Montreal. Glasserman, P. (2003), Monte Carlo methods in financial engineering, Springer Verlag, New York. Glasserman, P. and X. Zhao (1999), Arbitrage-free discretization of log-normal forward LIBOR and swap rate models, Finance and Stochastics, 4, pp. 35-68 Heston, S.L. (1993), A closed-form solution for options with stochastic volatility with applications to bond and currency options, Review of Financial Studies, vol. 6, no. 2, pp. 327-343. Johnson, N., S. Kotz, and N. Balakrishnan (1995), Continuous univariate distributions, vol. 2, Wiley Interscience. Kahl, C. and P. Jackel (2005), Fast strong approximation Monte-Carlo schemes for stochastic volatility models, Working Paper, ABN AMRO and University of Wuppertal. Lee, R. (2004), Option Pricing by Transform Methods: Extensions, Unification, and Error Control, Journal of Computational Finance, vol 7, issue 3, pp. 51-86 Lewis, A. (2001), Option valuation under stochastic volatility, Finance Press, Newport Beach. Lipton, A. (2002), The vol-smile problem, Risk Magazine, February, pp. 61-65. Lord, R., R. Koekkoek and D. van Dijk (2006), A Comparison of biased simulation schemes for stochastic volatility models, Working Paper, Tinbergen Institute. Kloeden, P. and E. Platen (1999), Numerical solution of stochastic differential equations, 3rd edition, Springer Verlag, New York. Moro, B. (1995), The full Monte, Risk Magazine, Vol.8, No.2, pp. 57-58. Patnaik, P. (1949), The non-central $\chi^{2}$ and F-distributions and their applications, Biometrika, 36, pp. 202-232. Pearson, E. (1959), Note on an approximation to the distribution of non-central $\chi^{2}$, Biometrika, 46, p. 364. Piterbarg, V. (2003), Discretizing Processes used in Stochastic Volatility Models, Working Paper, Bank of America. Piterbarg, V. (2005), Stochastic volatility model with time-dependent skew, Applied Mathematical Finance. Press, W., S. Teukolsky, W. Vetterling, and B. Flannery (1992), Numerical recipes in C, Cambridge University Press, New York |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/25645 |