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


  • Susanne Kruse


  • Ulrich Nögel



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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    Cited by:

    1. Elisa Alos & Antoine Jacquier & Jorge Leon, 2017. "The implied volatility of Forward-Start options: ATM short-time level, skew and curvature," Papers 1710.11232,
    2. Damien Ackerer & Damir Filipovic & Sergio Pulido, 2017. "The Jacobi Stochastic Volatility Model," Working Papers hal-01338330, HAL.
    3. 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.
    4. Fabio Antonelli & Alessandro Ramponi & Sergio Scarlatti, 2015. "Random Time Forward Starting Options," Papers 1504.03552,
    5. Elisa Alòs & Antoine Jacquier & Jorge A. León, 2017. "The implied volatility of forward starting options: ATM short-time level, skew and curvature," Economics Working Papers 1568, Department of Economics and Business, Universitat Pompeu Fabra.
    6. Damien Ackerer & Damir Filipovi'c & Sergio Pulido, 2016. "The Jacobi Stochastic Volatility Model," Papers 1605.07099,, revised Mar 2018.
    7. 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.


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