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

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