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Pricing of Pseudo-Swaps Based on Pseudo-Statistics

Author

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  • 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
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    References listed on IDEAS

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    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.
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