Robust Log-normal Stochastic Volatility for Interest Rate Dynamics

20 Pages Posted: 2 Jan 2023 Last revised: 30 Jan 2023

See all articles by Artur Sepp

Artur Sepp

Sygnum Bank Asset Management

Parviz Rakhmonov

Citigroup London

Date Written: December 31, 2022

Abstract

We introduce the log-normal stochastic volatility (SV) model for the dynamics of a short interest rate in the Cheyette model. We assume non-zero correlation between the dynamics of the short rate and the log-normal SV driver for modelling positive implied volatility skews observed in fixed-income derivatives. We show that our model is robust because the short rate process does not explode in finite time, in contrast to models which mix local rate dynamics with zero-correlated volatility dynamics. We obtain closed-form analytical solution for valuation of swaptions and for model calibration to market data. We show that our model is able both to fit accurately market implied volatilities and to be consistent with historical evolution of rates and volatilities.

Keywords: Interest rate volatility, log-normal stochastic volatility, Cheyette model

JEL Classification: G13, C63

Suggested Citation

Sepp, Artur and Rakhmonov, Parviz, Robust Log-normal Stochastic Volatility for Interest Rate Dynamics (December 31, 2022). Available at SSRN: https://ssrn.com/abstract=4315906 or http://dx.doi.org/10.2139/ssrn.4315906

Artur Sepp (Contact Author)

Sygnum Bank Asset Management ( email )

Uetlibergstrasse 134a
Zurich, 8045
Switzerland

HOME PAGE: http://artursepp.com

Parviz Rakhmonov

Citigroup London ( email )

33 Canada Square
London, E14 5LB
United Kingdom

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