A Methodology to Analyze Model Risk with an Application to Discount Bond Options in a Heath-Jarrow-Morton Framework

Risklab Research Report

42 Pages Posted: 10 Jul 2001

See all articles by Francois Lhabitant

Francois Lhabitant

Kedge Capital Fund Management; EDHEC Business School

Mireille Bossy

Institut National de Recherche en Informatique et Automatique (INRIA)

Rajna Gibson

University of Geneva - Geneva Finance Research Institute (GFRI)

Denis Talay

French National Institute for Research in Computer Science and Control (INRIA)

Nathalie Pistre

National Institute of Statistics and Economic Studies (INSEE) - National School for Statistical and Economic Administration (ENSAE)

Date Written: June 2001

Abstract

In this paper, we propose a general methodology to analyse model risk for discount bond options within a unified Heath, Jarrow, Morton (1992) framework. We illustrate its applicability by focusing on the hedging of discount bond options and options portfolios. We show how to decompose the agent's "model risk" profit and loss, and emphasize the importance of the position's gamma in order to control it. We further provide mathematical results on the distribution of the forward profit and loss function for specific Markov univariate term structure models. Finally, we run numerical simulations for naked and combined option's hedging strategies in order to quantify the sensitivity of the forward profit and loss function with respect to the volatility of the forward rate curve, the shape of the term structure, and the characteristics of the position being hedged.

Keywords: model risk, interest rate risk, Heath-Jarrow-Morton

JEL Classification: G13

Suggested Citation

Lhabitant, Francois-Serge and Bossy, Mireille and Gibson, Rajna and Talay, Denis and Pistre, Nathalie, A Methodology to Analyze Model Risk with an Application to Discount Bond Options in a Heath-Jarrow-Morton Framework (June 2001). Risklab Research Report. Available at SSRN: https://ssrn.com/abstract=275075 or http://dx.doi.org/10.2139/ssrn.275075

Francois-Serge Lhabitant (Contact Author)

Kedge Capital Fund Management ( email )

28-30 The Parade
St Helier, JE1 1ZZ
Jersey

HOME PAGE: http://www.lhabitant.net

EDHEC Business School ( email )

393 Prom. des Anglais
Nice, 06200
France

Mireille Bossy

Institut National de Recherche en Informatique et Automatique (INRIA)

40 avenue Halley
Villeneuve, 59650
France

Rajna Gibson

University of Geneva - Geneva Finance Research Institute (GFRI) ( email )

40 Boulevard du Pont d'Arve
Geneva 4, 1211
Switzerland
+41.22.379.89.83 (Phone)

Denis Talay

French National Institute for Research in Computer Science and Control (INRIA) ( email )

2004 route des Lucioles
BP 94
06902 Sophia Antipolis Cedex
France

Nathalie Pistre

National Institute of Statistics and Economic Studies (INSEE) - National School for Statistical and Economic Administration (ENSAE) ( email )

92245 Malakoff Cedex
France

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