IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v11y2023i8p141-d1209402.html
   My bibliography  Save this article

Pricing of Pseudo-Swaps Based on Pseudo-Statistics

Author

Listed:
  • Sebastian Franco

    (Department of Mathematics and Statistics, University of Calgary, Calgary, AB T2N 1N4, Canada
    These authors contributed equally to this work.)

  • Anatoliy Swishchuk

    (Department of Mathematics and Statistics, University of Calgary, Calgary, AB T2N 1N4, Canada
    These authors contributed equally to this work.)

Abstract

The main problem in pricing variance, volatility, and correlation swaps is how to determine the evolution of the stochastic processes for the underlying assets and their volatilities. Thus, sometimes it is simpler to consider pricing of swaps by so-called pseudo-statistics, namely, the pseudo-variance, -covariance, -volatility, and -correlation. The main motivation of this paper is to consider the pricing of swaps based on pseudo-statistics, instead of stochastic models, and to compare this approach with the most popular stochastic volatility model in the Cox–Ingresoll–Ross (CIR) model. Within this paper, we will demonstrate how to value different types of swaps (variance, volatility, covariance, and correlation swaps) using pseudo-statistics (pseudo-variance, pseudo-volatility, pseudo-correlation, and pseudo-covariance). As a result, we will arrive at a method for pricing swaps that does not rely on any stochastic models for a stochastic stock price or stochastic volatility, and instead relies on data/statistics. A data/statistics-based approach to swap pricing is very different from stochastic volatility models such as the Cox–Ingresoll–Ross (CIR) model, which, in comparison, follows a stochastic differential equation. Although there are many other stochastic models that provide an approach to calculating the price of swaps, we will use the CIR model for comparison within this paper, due to the popularity of the CIR model. Therefore, in this paper, we will compare the CIR model approach to pricing swaps to the pseudo-statistic approach to pricing swaps, in order to compare a stochastic model to the data/statistics-based approach to swap pricing that is developed within this paper.

Suggested Citation

  • Sebastian Franco & Anatoliy Swishchuk, 2023. "Pricing of Pseudo-Swaps Based on Pseudo-Statistics," Risks, MDPI, vol. 11(8), pages 1-30, August.
    • Handle: RePEc:gam:jrisks:v:11:y:2023:i:8:p:141-:d:1209402
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/11/8/141/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-9091/11/8/141/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jeff Fleming & Barbara Ostdiek & Robert E. Whaley, 1995. "Predicting stock market volatility: A new measure," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 15(3), pages 265-302, May.
    2. Fred Espen Benth & Martin Groth & Rodwell Kufakunesu, 2007. "Valuing Volatility and Variance Swaps for a Non-Gaussian Ornstein-Uhlenbeck Stochastic Volatility Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(4), pages 347-363.
    3. Galai, Dan, 1979. "A Proposal for Indexes for Traded Call Options," Journal of Finance, American Finance Association, vol. 34(5), pages 1157-1172, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Carol Alexander & Julia Kapraun & Dimitris Korovilas, 2015. "Trading and Investing in Volatility Products," Financial Markets, Institutions & Instruments, John Wiley & Sons, vol. 24(4), pages 313-347, November.
    2. Juliusz Jablecki & Robert Slepaczuk & Ryszard Kokoszczynski & Pawel Sakowski & Piotr Wojcik, 2014. "Does historical VIX term structure contain valuable information for predicting VIX futures?," Dynamic Econometric Models, Uniwersytet Mikolaja Kopernika, vol. 14, pages 5-28.
    3. Agbeyegbe, Terence D., 2015. "An inverted U-shaped crude oil price return-implied volatility relationship," Review of Financial Economics, Elsevier, vol. 27(C), pages 28-45.
    4. Xuan Vinh Vo & Kevin Daly, 2008. "Volatility amongst firms in the Dow Jones Eurostoxx50 Index," Applied Financial Economics, Taylor & Francis Journals, vol. 18(7), pages 569-582.
    5. Carole Bernard & Zhenyu Cui, 2013. "Prices and Asymptotics for Discrete Variance Swaps," Papers 1305.7092, arXiv.org.
    6. Piotr Szczepocki, 2020. "Application of iterated filtering to stochastic volatility models based on non-Gaussian Ornstein-Uhlenbeck process," Statistics in Transition New Series, Polish Statistical Association, vol. 21(2), pages 173-187, June.
    7. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    8. Kian-Guan Lim & Michelle Lim, 2020. "Financial performance of shipping firms that increase LNG carriers and the support of eco-innovation," Journal of Shipping and Trade, Springer, vol. 5(1), pages 1-25, December.
    9. Siriopoulos, Costas & Fassas, Athanasios, 2012. "An investor sentiment barometer — Greek Implied Volatility Index (GRIV)," Global Finance Journal, Elsevier, vol. 23(2), pages 77-93.
    10. 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;The Institute of Statistical Mathematics, vol. 65(1), pages 89-103, February.
    11. Shin-Yun Wang & Ming-Che Chuang & Shih-Kuei Lin & So-De Shyu, 2021. "Option pricing under stock market cycles with jump risks: evidence from the S&P 500 index," Review of Quantitative Finance and Accounting, Springer, vol. 56(1), pages 25-51, January.
    12. Sayantan Khanra & Sanjay Dhir, 2017. "Creating Value in Small-cap Firms by Mitigating Risks of Market Volatility," Vision, , vol. 21(4), pages 350-355, December.
    13. Saffet Akdag & Ömer İskenderoglu & Andrew Adewale Alola, 2020. "The volatility spillover effects among risk appetite indexes: insight from the VIX and the rise," Letters in Spatial and Resource Sciences, Springer, vol. 13(1), pages 49-65, April.
    14. Papadamou, Stephanos & Fassas, Athanasios P. & Kenourgios, Dimitris & Dimitriou, Dimitrios, 2023. "Effects of the first wave of COVID-19 pandemic on implied stock market volatility: International evidence using a google trend measure," The Journal of Economic Asymmetries, Elsevier, vol. 28(C).
    15. Fernandez-Perez, Adrian & Frijns, Bart & Tourani-Rad, Alireza, 2017. "When no news is good news – The decrease in investor fear after the FOMC announcement," Journal of Empirical Finance, Elsevier, vol. 41(C), pages 187-199.
    16. Chen, Zhengyang, 2019. "The Long-term Rate and Interest Rate Volatility in Monetary Policy Transmission," MPRA Paper 96339, University Library of Munich, Germany.
    17. Alexander, Carol & Prokopczuk, Marcel & Sumawong, Anannit, 2013. "The (de)merits of minimum-variance hedging: Application to the crack spread," Energy Economics, Elsevier, vol. 36(C), pages 698-707.
    18. Kawai Reiichiro & Masuda Hiroki, 2011. "Exact discrete sampling of finite variation tempered stable Ornstein–Uhlenbeck processes," Monte Carlo Methods and Applications, De Gruyter, vol. 17(3), pages 279-300, January.
    19. Philip Stahl, 2022. "Asymptotic extrapolation of model-free implied variance: exploring structural underestimation in the VIX Index," Review of Derivatives Research, Springer, vol. 25(3), pages 315-339, October.
    20. Jozef Barunik & Mattia Bevilacqua & Radu Tunaru, 2022. "Asymmetric Network Connectedness of Fears," The Review of Economics and Statistics, MIT Press, vol. 104(6), pages 1304-1316, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jrisks:v:11:y:2023:i:8:p:141-:d:1209402. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.