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On the pricing of forward starting options in Heston’s model on stochastic volatility

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  • Susanne Kruse

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  • Ulrich Nögel

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Abstract

We consider the problem of pricing European forward starting options in the presence of stochastic volatility. By performing a change of measure using the asset price at the time of strike determination as a numeraire, we derive a closed-form solution within Heston’s stochastic volatility framework applying distribution properties of the volatility process. In this paper we develop a new and more suitable formula for pricing forward starting options. This formula allows to cover the smile effects observed in a Black-Scholes environment, in which the extreme exposure of forward starting options to volatility changes is ignored. Copyright Springer-Verlag Berlin/Heidelberg 2005

Suggested Citation

  • Susanne Kruse & Ulrich Nögel, 2005. "On the pricing of forward starting options in Heston’s model on stochastic volatility," Finance and Stochastics, Springer, vol. 9(2), pages 233-250, April.
  • Handle: RePEc:spr:finsto:v:9:y:2005:i:2:p:233-250 DOI: 10.1007/s00780-004-0146-3
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    References listed on IDEAS

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    1. Ai[diaeresis]t-Sahalia, Yacine & Kimmel, Robert, 2007. "Maximum likelihood estimation of stochastic volatility models," Journal of Financial Economics, Elsevier, vol. 83(2), pages 413-452, February.
    2. Arnaud Gloter, 2006. "Parameter Estimation for a Discretely Observed Integrated Diffusion Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(1), pages 83-104.
    3. Ole E. Barndorff-Nielsen & Neil Shephard, 2004. "Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics," Econometrica, Econometric Society, vol. 72(3), pages 885-925, May.
    4. Bollerslev, Tim & Zhou, Hao, 2002. "Estimating stochastic volatility diffusion using conditional moments of integrated volatility," Journal of Econometrics, Elsevier, vol. 109(1), pages 33-65, July.
    5. Yacine Ait-Sahalia & Robert Kimmel, 2004. "Maximum Likelihood Estimation of Stochastic Volatility Models," NBER Working Papers 10579, National Bureau of Economic Research, Inc.
    6. Peter C.B. Phillips & Jun Yu, 2005. "A Two-Stage Realized Volatility Approach to the Estimation for Diffusion Processes from Discrete Observations," Cowles Foundation Discussion Papers 1523, Cowles Foundation for Research in Economics, Yale University.
    7. Yoshida, Nakahiro, 1992. "Estimation for diffusion processes from discrete observation," Journal of Multivariate Analysis, Elsevier, vol. 41(2), pages 220-242, May.
    8. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
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    Cited by:

    1. Susanne Griebsch & Uwe Wystup, 2011. "On the valuation of fader and discrete barrier options in Heston's stochastic volatility model," Quantitative Finance, Taylor & Francis Journals, vol. 11(5), pages 693-709.
    2. Elisa Alos & Antoine Jacquier & Jorge Leon, 2017. "The implied volatility of Forward-Start options: ATM short-time level, skew and curvature," Papers 1710.11232, arXiv.org.
    3. Damien Ackerer & Damir Filipovic & Sergio Pulido, 2017. "The Jacobi Stochastic Volatility Model," Working Papers hal-01338330, HAL.
    4. Damien Ackerer & Damir Filipovi'c & Sergio Pulido, 2016. "The Jacobi Stochastic Volatility Model," Papers 1605.07099, arXiv.org, revised Jul 2017.
    5. Coqueret, Guillaume & Tavin, Bertrand, 2016. "An investigation of model risk in a market with jumps and stochastic volatility," European Journal of Operational Research, Elsevier, vol. 253(3), pages 648-658.
    6. Elisa Alòs & Antoine Jacquier & Jorge A. León, 2017. "The Implied Volatility of Forward Starting Options: ATM Short-Time Level, Skew and Curvature," Working Papers 988, Barcelona Graduate School of Economics.
    7. Fabio Antonelli & Alessandro Ramponi & Sergio Scarlatti, 2015. "Random Time Forward Starting Options," Papers 1504.03552, arXiv.org.

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