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Expressions of forward starting option price in Hull–White stochastic volatility model

Author

Listed:
  • Hiroaki Hata

    (Hitotsubashi University)

  • Nien-Lin Liu

    (Tokyo University of Science)

  • Kazuhiro Yasuda

    (Hosei University)

Abstract

We are interested in problems related to forward starting options for Hull–White stochastic volatility model. Our objective is to obtain analytical, semi-analytical, or approximated expressions of its price for simulation. To obtain an analytical representation of the price, we use Yor’s formula. However, the analytical formula is difficult to implement. Next we consider semi-analytical expressions for the price. In order to have them, we use the tower property for conditional expectations with a certain filtration and explicitly calculate it. Then, we consider an expansion expression for the price using the semi-analytical expression to have a simple expression. The semi-analytical expressions and the expansion expression can reduce computational costs and standard errors when the Monte Carlo method is used. Finally, some numerical results are given to show their accuracy and efficiency.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:decfin:v:45:y:2022:i:1:d:10.1007_s10203-021-00343-w
    DOI: 10.1007/s10203-021-00343-w
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    References listed on IDEAS

    as
    1. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
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    3. Peter G Zhang, 1998. "Exotic Options:A Guide to Second Generation Options," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 3800, January.
    4. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    5. 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.
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    More about this item

    Keywords

    Forward starting option; Hull–White stochastic volatility model; Yor’s formula; Asymptotic expansion;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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