Asymptotic Analysis for One-Name Credit Derivatives

Yong-Ki Ma,Beom Jin Kim

doi:10.1155/2013/567340

Yong-Ki Ma, Beom Jin Kim

Open Access

https://doi.org/10.1155/2013/567340

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Abstract

We propose approximate solutions to price defaultable zero-coupon bonds as well as the corresponding credit default swaps and bond options. We consider the intensity-based approach of a two-correlated-factor Hull-White model with stochastic volatility of interest rate process. Perturbations from the stochastic volatility are computed by using an asymptotic analysis. We also study the sensitive properties of the defaultable bond prices and the yield curves.

Highlights

We review the price of the defaultable zero-coupon bonds when the interest rate process and the intensity process are correlated and each of these processes follows a Hull-White model [24]
We present an asymptotic analysis to the solution of the partial differential equation (PDE) (8) and give an approximate solution of the defaultable zerocoupon bond price for ε
We calculate the magnitude of mispricing with respect to defaultable zero-coupon bonds as a percentage of the face value of bond

Summary

Introduction

It is well known that the methodology for modeling a credit risk can be split into two primary approaches of models that attempt to describe default processes (see Duffie and Singleton [1] and Bielecki and Rutkowski [2] for general references): the structural approach such as those developed by Merton [3], Longstaff and Schwartz [4], Leland and Toft [5], Zhou [6], Duffie and Lando [7], Hilberink and Rogers [8], and Giesecke [9] and the intensity-based approach such as those developed by Jarrow and Turnbull [10], Madan and Unal [11], Lando [12], Duffie and Singleton [13], and CollinDufresne and Goldstein [14]. Schonbucher [15] develops the term structure model of defaultable interest rates by using the Heath-Jarrow-Morton model, and Tchuindjo [16] studies the price of a defaultable zero-coupon bond with two-correlated-factor Hull-White model. Tchuindjo [16] studies the two-correlated-factor Hull-White model to propose a closed-form solution to price the defaultable bonds, supposing a nonzero correlation between interest rate process and intensity process. We expand the twocorrelated-factor Hull-White model by modifying constant volatility of interest rate process and use an asymptotic analysis for prices of the defaultable zero-coupon bonds. Our numerical results indicate that the defaultable zero-coupon bonds with stochastic volatility of interest rate process affects both quantitative and qualitative effect.

Defaultable Zero-Coupon Bonds

Asymptotic Analysis

Pricing Credit Default Swaps and Bond Options

Final Remarks