Stochastic Interest Rates for Local Volatility Hybrids Models

10 Pages Posted: 19 Mar 2008  

Eric Benhamou

Université Paris Est - Université Paris Est-Creteil

Arnaud Rivoira

Supélec

Anne Gruz

Misys Summit

Date Written: March 17 2008

Abstract

This paper studies the impact of stochastic interest rates for local volatility hybrids. Our research shows that it is possible to explicitly determine the bias between the local volatility of a model with stochastic interest rates and the local volatility of the same model, but with deterministic interest rates as a function between the correlation of the stochastic interest rates and the digital at the local strike. The paper will show that this bias can be expressed in a simpler form under the assumption of a diffusion of the stochastic interest rates, enabling us to compute a fast calibration for a hybrid model with stochastic interest rates. This bias leads to a decrease in the value of the local volatility as a result of the induced volatility caused by the stochastic drift. Numerical results illustrate the importance of the bias and confirm that some stochastic noise arises from the stochastic drift.

Keywords: local volatility, stochastic interest rates, hybrid, Malliavin calculus

JEL Classification: G12, G13

Suggested Citation

Benhamou, Eric and Rivoira, Arnaud and Gruz, Anne, Stochastic Interest Rates for Local Volatility Hybrids Models (March 17 2008). Available at SSRN: https://ssrn.com/abstract=1107711 or http://dx.doi.org/10.2139/ssrn.1107711

Eric Benhamou (Contact Author)

Université Paris Est - Université Paris Est-Creteil ( email )

61 avenue du Général de Gaulle
Créteil, 940000
France

Arnaud Rivoira

Supélec ( email )

Plateau du Moulon
3 rue Joliot-Curie
Gif sur Yvette Cedex, 91192
France

Anne Gruz

Misys Summit ( email )

63, Boulevard Haussmann
Paris, IDF 75008
France
0033144782828 (Phone)

HOME PAGE: http://www.misys.com/

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