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Fractional Barndorff-Nielsen and Shephard model: applications in variance and volatility swaps, and hedging

Author

Listed:
  • Nicholas Salmon

    (North Dakota State University)

  • Indranil SenGupta

    (North Dakota State University)

Abstract

In this paper, we introduce and analyze the fractional Barndorff-Nielsen and Shephard (BN-S) stochastic volatility model. The proposed model is based upon two desirable properties of the long-term variance process suggested by the empirical data: long-term memory and jumps. The proposed model incorporates the long-term memory and positive autocorrelation properties of fractional Brownian motion with $$H>1/2$$ H > 1 / 2 , and the jump properties of the BN-S model. We find arbitrage-free prices for variance and volatility swaps for this new model. Because fractional Brownian motion is still a Gaussian process, we derive some new expressions for the distributions of integrals of continuous Gaussian processes as we work towards an analytic expression for the prices of these swaps. The model is analyzed in connection to the quadratic hedging problem and some related analytical results are developed. The amount of derivatives required to minimize a quadratic hedging error is obtained. Finally, we provide some numerical analysis based on the VIX data. Numerical results show the efficiency of the proposed model compared to the Heston model and the classical BN-S model.

Suggested Citation

  • Nicholas Salmon & Indranil SenGupta, 2021. "Fractional Barndorff-Nielsen and Shephard model: applications in variance and volatility swaps, and hedging," Annals of Finance, Springer, vol. 17(4), pages 529-558, December.
    • Handle: RePEc:kap:annfin:v:17:y:2021:i:4:d:10.1007_s10436-021-00394-4
    DOI: 10.1007/s10436-021-00394-4
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    Cited by:

    1. Sivajiganesan Sivasankar & Ramalingam Udhayakumar & Velmurugan Subramanian & Ghada AlNemer & Ahmed M. Elshenhab, 2022. "Existence of Hilfer Fractional Stochastic Differential Equations with Nonlocal Conditions and Delay via Almost Sectorial Operators," Mathematics, MDPI, vol. 10(22), pages 1-18, November.
    2. Xianfei Hui & Baiqing Sun & Indranil SenGupta & Yan Zhou & Hui Jiang, 2022. "Stochastic volatility modeling of high-frequency CSI 300 index and dynamic jump prediction driven by machine learning," Papers 2204.02891, arXiv.org, revised Jan 2023.
    3. Minglian Lin & Indranil SenGupta, 2023. "Analysis of optimal portfolio on finite and small-time horizons for a stochastic volatility model with multiple correlated assets," Papers 2302.06778, arXiv.org, revised Dec 2023.
    4. Xianfei Hui & Baiqing Sun & Hui Jiang & Yan Zhou, 2022. "Modeling dynamic volatility under uncertain environment with fuzziness and randomness," Papers 2204.12657, arXiv.org, revised Oct 2022.

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    More about this item

    Keywords

    Fractional Brownian motion; Young integral; Ornstein-Uhlenbeck process; Swaps; Quadratic hedging;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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