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Valuing Volatility and Variance Swaps for a Non-Gaussian Ornstein-Uhlenbeck Stochastic Volatility Model

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  • Fred Espen Benth
  • Martin Groth
  • Rodwell Kufakunesu
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    Abstract

    Following the increasing awareness of the risk from volatility fluctuations, the market for hedging contracts written on realized volatility has surged. Companies looking for means to secure against unexpected accumulation of market activity can find over-the-counter products written on volatility indices. Since the Black and Scholes model require a constant volatility the need to consider other models is obvious. Swaps written on powers of realized volatility in the stochastic volatility model proposed by Barndorff-Nielsen and Shephard are investigated. A key formula is derived for the realized variance able to represent the swap price dynamics in terms of Laplace transforms, which makes fast numerical inversion methods viable. An example using the fast Fourier transform is shown and compared with the approximation proposed by Brockhaus and Long.

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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

    Volume (Year): 14 (2007)
    Issue (Month): 4 ()
    Pages: 347-363

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    Handle: RePEc:taf:apmtfi:v:14:y:2007:i:4:p:347-363

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    Related research

    Keywords: Risk; hedging contracts; realized volatility; stochastic volatility; Levy processes; Laplace transforms;

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    Cited by:
    1. Imai, Junichi & Kawai, Reiichiro, 2011. "On finite truncation of infinite shot noise series representation of tempered stable laws," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4411-4425.
    2. Friedrich Hubalek & Martin Keller-Ressel & Carlo Sgarra, 2014. "Geometric Asian Option Pricing in General Affine Stochastic Volatility Models with Jumps," Papers 1407.2514, arXiv.org.
    3. Shibin Zhang & Xinsheng Zhang, 2013. "A least squares estimator for discretely observed Ornstein–Uhlenbeck processes driven by symmetric α-stable motions," Annals of the Institute of Statistical Mathematics, Springer, vol. 65(1), pages 89-103, February.
    4. Giovanni Salvi & Anatoliy V. Swishchuk, 2012. "Modeling and Pricing of Covariance and Correlation Swaps for Financial Markets with Semi-Markov Volatilities," Papers 1205.5565, arXiv.org.
    5. Carole Bernard & Zhenyu Cui, 2013. "Prices and Asymptotics for Discrete Variance Swaps," Papers 1305.7092, arXiv.org.

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