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Asymptotic and Exact Pricing of Options on Variance

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  • Martin Keller-Ressel
  • Johannes Muhle-Karbe

Abstract

We consider the pricing of derivatives written on the discretely sampled realized variance of an underlying security. In the literature, the realized variance is usually approximated by its continuous-time limit, the quadratic variation of the underlying log-price. Here, we characterize the small-time limits of options on both objects. We find that the difference between them strongly depends on whether or not the stock price process has jumps. Subsequently, we propose two new methods to evaluate the price of options on the discretely sampled realized variance. One of the methods is approximative; it is based on correcting prices of options on quadratic variation by our asymptotic results. The other method is exact; it uses a novel randomization approach and applies Fourier-Laplace techniques. We compare the methods and illustrate our results by some numerical examples.

Suggested Citation

  • Martin Keller-Ressel & Johannes Muhle-Karbe, 2010. "Asymptotic and Exact Pricing of Options on Variance," Papers 1003.5514, arXiv.org, revised Nov 2010.
    • Handle: RePEc:arx:papers:1003.5514
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    Cited by:

    1. Wendong Zheng & Yue Kuen Kwok, 2014. "Saddlepoint Approximation Methods for Pricing Derivatives on Discrete Realized Variance," Applied Mathematical Finance, Taylor & Francis Journals, vol. 21(1), pages 1-31, March.
    2. Alexander M. G. Cox & Jiajie Wang, 2011. "Root's barrier: Construction, optimality and applications to variance options," Papers 1104.3583, arXiv.org, revised Mar 2013.

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