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Analysis of variance based instruments for Ornstein–Uhlenbeck type models: swap and price index

Author

Listed:
  • Aziz Issaka

    (North Dakota State University)

  • Indranil SenGupta

    (North Dakota State University)

Abstract

In this paper a couple of variance dependent instruments in the financial market are studied. Firstly, a number of aspects of the variance swap in connection to the Barndorff-Nielsen and Shephard model are studied. A partial integro-differential equation that describes the dynamics of the arbitrage-free price of the variance swap is formulated. Under appropriate assumptions for the first four cumulants of the driving subordinator, a Večeř-type theorem is proved. The bounds of the arbitrage-free variance swap price are also found. Finally, a price-weighted index modulated by market variance is introduced. The large-basket limit dynamics of the price index and the “error term” are derived. Empirical data driven numerical examples are provided in support of the proposed price index.

Suggested Citation

  • Aziz Issaka & Indranil SenGupta, 2017. "Analysis of variance based instruments for Ornstein–Uhlenbeck type models: swap and price index," Annals of Finance, Springer, vol. 13(4), pages 401-434, November.
    • Handle: RePEc:kap:annfin:v:13:y:2017:i:4:d:10.1007_s10436-017-0302-3
    DOI: 10.1007/s10436-017-0302-3
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    References listed on IDEAS

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    4. Indranil SenGupta & William Nganje & Erik Hanson, 2021. "Refinements of Barndorff-Nielsen and Shephard Model: An Analysis of Crude Oil Price with Machine Learning," Annals of Data Science, Springer, vol. 8(1), pages 39-55, March.
    5. Massimiliano Ferrara & Bruno A. Pansera & Francesco Strati, 2017. "On the Inception of Financial Representative Bubbles," Mathematics, MDPI, vol. 5(4), pages 1-9, November.
    6. Humayra Shoshi & Indranil SenGupta, 2020. "Hedging and machine learning driven crude oil data analysis using a refined Barndorff-Nielsen and Shephard model," Papers 2004.14862, arXiv.org, revised Feb 2021.
    7. Chen Mao & Guanqi Liu & Yuwen Wang, 2021. "A Closed-Form Pricing Formula for Log-Return Variance Swaps under Stochastic Volatility and Stochastic Interest Rate," Mathematics, MDPI, vol. 10(1), pages 1-17, December.
    8. Gong, Yaxian, 2020. "Credit default swap and two-sided moral hazard," Finance Research Letters, Elsevier, vol. 34(C).
    9. Michael Roberts & Indranil SenGupta, 2020. "Sequential hypothesis testing in machine learning, and crude oil price jump size detection," Papers 2004.08889, arXiv.org, revised Dec 2020.
    10. Shantanu Awasthi & Indranil SenGupta, 2020. "First exit-time analysis for an approximate Barndorff-Nielsen and Shephard model with stationary self-decomposable variance process," Papers 2006.07167, arXiv.org, revised Jan 2021.
    11. Nicholas Salmon & Indranil SenGupta, 2021. "Fractional Barndorff-Nielsen and Shephard model: applications in variance and volatility swaps, and hedging," Papers 2105.02325, arXiv.org.
    12. Nikolai Dokuchaev, 2018. "On the implied market price of risk under the stochastic numéraire," Annals of Finance, Springer, vol. 14(2), pages 223-251, May.
    13. Xin-Jiang He & Song-Ping Zhu, 2019. "Variance And Volatility Swaps Under A Two-Factor Stochastic Volatility Model With Regime Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(04), pages 1-19, June.
    14. Michael Roberts & Indranil SenGupta, 2020. "Infinitesimal generators for two-dimensional Lévy process-driven hypothesis testing," Annals of Finance, Springer, vol. 16(1), pages 121-139, March.
    15. Takuji Arai, 2019. "Pricing And Hedging Of Vix Options For Barndorff-Nielsen And Shephard Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(08), pages 1-26, December.
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    19. Xu, De-xuan & Yang, Ben-zhang & Kang, Jian-hao & Huang, Nan-jing, 2021. "Variance and volatility swaps valuations with the stochastic liquidity risk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
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    21. Takuji Arai, 2019. "Pricing and hedging of VIX options for Barndorff-Nielsen and Shephard models," Papers 1904.12260, arXiv.org.

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    More about this item

    Keywords

    Barndorff-Nielsen and Shephard model; Variance swap; Stochastic volatility; Price index; Weak convergence;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • L16 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Industrial Organization and Macroeconomics; Macroeconomic Industrial Structure

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