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Variance and volatility swaps and options under the exponential fractional Ornstein–Uhlenbeck model

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  • Kim, Hyun-Gyoon
  • Kim, See-Woo
  • Kim, Jeong-Hoon

Abstract

Considering the fair strike values of variance and volatility swaps, we use a stochastic volatility model in which the log volatility is given by a fractional Ornstein–Uhlenbeck process with two versions; a stationary version and a version with a deterministic initial value. Under these versions, the fair strike formulas are obtained in exact form for variance swaps and approximated fair strike formulas are derived for volatility swaps based on the fact that an aggregation of log-normal variables is well-approximated by shifted log-normal or log-normal distribution. In addition, we obtain two approximate pricing formulas for European options on the realized variance and volatility. The accuracy and robustness of the approximated fair strike formulas are examined via Monte-Carlo computations. We conduct calibration experiments to show that the Hurst exponent and the mean-reversion property of the fractional Ornstein–Uhlenbeck process are able to produce various shapes resembling the market term-structures of variance swaps when they are put together.

Suggested Citation

  • Kim, Hyun-Gyoon & Kim, See-Woo & Kim, Jeong-Hoon, 2024. "Variance and volatility swaps and options under the exponential fractional Ornstein–Uhlenbeck model," The North American Journal of Economics and Finance, Elsevier, vol. 72(C).
    • Handle: RePEc:eee:ecofin:v:72:y:2024:i:c:s1062940824000809
    DOI: 10.1016/j.najef.2024.102155
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    1. Boris Ter-Avanesov & Gunter A. Meissner, 2024. "Pricing Multi-strike Quanto Call Options on Multiple Assets with Stochastic Volatility, Correlation, and Exchange Rates," Papers 2411.16617, arXiv.org.

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    More about this item

    Keywords

    Variance swap; Volatility swap; Fractional Ornstein–Uhlenbeck process; Shifted log-normal approximation; Log-normal approximation;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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