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

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  • Susanne Kruse
  • Ulrich Nögel

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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    Citations

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    Cited by:

    1. Susanne Griebsch & Uwe Wystup, 2011. "Quantitative Finance, Vol. 11, No. 5, May 2011, 693-709 On the valuation of fader and discrete barrier options in Heston's stochastic volatility model," Quantitative Finance, Taylor & Francis Journals, vol. 11(8), pages 1271-1271.
    2. Martin Friesen & Sven Karbach, 2024. "Stationary covariance regime for affine stochastic covariance models in Hilbert spaces," Finance and Stochastics, Springer, vol. 28(4), pages 1077-1116, October.
    3. Lazar, Emese & Qi, Shuyuan, 2022. "Model risk in the over-the-counter market," European Journal of Operational Research, Elsevier, vol. 298(2), pages 769-784.
    4. Mark Broadie & Özgür Kaya, 2006. "Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes," Operations Research, INFORMS, vol. 54(2), pages 217-231, April.
    5. Damien Ackerer & Damir Filipović & Sergio Pulido, 2018. "The Jacobi stochastic volatility model," Finance and Stochastics, Springer, vol. 22(3), pages 667-700, July.
    6. 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.
    7. Lin, Sha & He, Xin-Jiang, 2021. "A closed-form pricing formula for forward start options under a regime-switching stochastic volatility model," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    8. F. Antonelli & A. Ramponi & S. Scarlatti, 2016. "Random Time Forward-Starting Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(08), pages 1-25, December.
    9. 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.
    10. Damir Filipovic & Damien Ackerer & Sergio Pulido, 2018. "The Jacobi Stochastic Volatility Model," Post-Print hal-01338330, HAL.
    11. Damien Ackerer & Damir Filipovic & Sergio Pulido, 2017. "The Jacobi Stochastic Volatility Model," Working Papers hal-01338330, HAL.
    12. Damien Ackerer & Damir Filipovi'c & Sergio Pulido, 2016. "The Jacobi Stochastic Volatility Model," Papers 1605.07099, arXiv.org, revised Mar 2018.
    13. Jia-Hau Guo & Mao-Wei Hung, 2007. "A Note on the Discontinuity Problem in Heston's Stochastic Volatility Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(4), pages 339-345.
    14. 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.
    15. 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 School of Economics.
    16. José L. Vilar-Zanón & Barbara Rogo, 2024. "Pricing and Hedging Contingent Claims by Entropy Segmentation and Fenchel Duality," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-20, December.
    17. João Pedro Vidal Nunes & Tiago Ramalho Viegas Alcaria, 2016. "Valuation of forward start options under affine jump-diffusion models," Quantitative Finance, Taylor & Francis Journals, vol. 16(5), pages 727-747, May.
    18. Sanjay K. Nawalkha & Xiaoyang Zhuo, 2022. "A Theory of Equivalent Expectation Measures for Contingent Claim Returns," Journal of Finance, American Finance Association, vol. 77(5), pages 2853-2906, October.
    19. Hiroaki Hata & Nien-Lin Liu & Kazuhiro Yasuda, 2022. "Expressions of forward starting option price in Hull–White stochastic volatility model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 101-135, June.

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