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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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    Cited by:

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    3. Liang Wang & Weixuan Xia, 2022. "Power‐type derivatives for rough volatility with jumps," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(7), pages 1369-1406, July.
    4. 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.
    5. Gong, Yaxian, 2020. "Credit default swap and two-sided moral hazard," Finance Research Letters, Elsevier, vol. 34(C).
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Xianfei Hui & Baiqing Sun & Hui Jiang & Indranil SenGupta, 2021. "Analysis of stock index with a generalized BN-S model: an approach based on machine learning and fuzzy parameters," Papers 2101.08984, arXiv.org, revised Feb 2022.
    11. Semere Habtemicael & Musie Ghebremichael & Indranil SenGupta, 2019. "Volatility and Variance Swap Using Superposition of the Barndorff-Nielsen and Shephard type Lévy Processes," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 75-92, June.
    12. 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.
    13. Michael Roberts & Indranil SenGupta, 2019. "Infinitesimal generators for two-dimensional L\'evy process-driven hypothesis testing," Papers 1911.08412, arXiv.org.
    14. Takuji Arai, 2019. "Pricing and hedging of VIX options for Barndorff-Nielsen and Shephard models," Papers 1904.12260, arXiv.org.
    15. Massimiliano Ferrara & Bruno A. Pansera & Francesco Strati, 2017. "On the Inception of Financial Representative Bubbles," Mathematics, MDPI, vol. 5(4), pages 1-9, November.
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    19. 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.
    20. 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.
    21. 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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    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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