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Local Volatility in Interest Rate Models

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  • V. M. Belyaev

Abstract

Local Volatility (LV) is a very powerful tool for market modeling. This tool can be used to generate arbitrage-free scenarios calibrated to all available options. Here we demonstrate how to implement LV in order to reproduce most swaption prices within a single model. There was a good agreement between market prices and Monte Carlo prices for all tenors and maturities from 2 to 20 years. Note that due to the use of a normal distribution in the scenario generation process, the volatility of short-term swaptions cannot be generated accurately.

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  • V. M. Belyaev, 2023. "Local Volatility in Interest Rate Models," Papers 2301.13595, arXiv.org, revised Mar 2024.
    • Handle: RePEc:arx:papers:2301.13595
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    1. Heath, David & Jarrow, Robert & Morton, Andrew, 1990. "Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(4), pages 419-440, December.
    2. Viorel Costeanu & Dan Pirjol, 2011. "Asymptotic Expansion for the Normal Implied Volatility in Local Volatility Models," Papers 1105.3359, arXiv.org.
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