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Analytic RFR Option Pricing with Smile and Skew

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  • Colin Turfus
  • Aurelio Romero-Berm'udez

Abstract

We extend the short rate model of Turfus and Romero-Berm\'udez [2021] to facilitate accurate arbitrage-free analytic pricing of SOFR, SONIA or ESTR caplets, i.e. options on backward-looking compounded rates payments, in a manner consistent with the smile and skew levels observed in the market. These caplet pricing formulae and corresponding LIBOR or term-rate caplet results are translated into effective variance (implied volatility) formulae, which are seen to be of a particularly simple form. They show that the model is essentially equivalent to imposing on a Hull-White model an effective variance which is a quadratic function of the moneyness parameter (rather than a constant) for any given maturity. Results are also illustrated graphically.

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  • Colin Turfus & Aurelio Romero-Berm'udez, 2023. "Analytic RFR Option Pricing with Smile and Skew," Papers 2301.01260, arXiv.org.
    • Handle: RePEc:arx:papers:2301.01260
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    References listed on IDEAS

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    1. C. Turfus, 2019. "Closed-form Arrow-Debreu pricing for the Hull-White short rate model," Quantitative Finance, Taylor & Francis Journals, vol. 19(12), pages 2087-2094, December.
    2. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    3. Elisa Alòs & Rafael De Santiago & Josep Vives, 2015. "Calibration Of Stochastic Volatility Models Via Second-Order Approximation: The Heston Case," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(06), pages 1-31.
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