A Valuation Model Of Credit-rating Linked
Coupon Bond Based On A Structural Model
Author(s)
K. Yahagi & K. Miyazaki
Abstract
A credit-linked coupon bond pays a coupon associated with its credit rating at
the time of the coupon payment date, rather than an amount equal to the initially
fixed coupon. The only existing corporate bond valuation model for creditrating-
triggered products was formulated by Jarrow et al. However, this model
does not incorporate the fact that increases in the coupon payment resulting from
downgrades may cause a further deterioration of credit ratings and of the
likelihood that the company will be able to make future coupon payments. In this
paper, we present a credit-linked coupon bond valuation model that considers
this issue. Using a structural approach, we extend the classical model of Merton
by introducing a threshold value corresponding to each credit rating, and a
volatility of the company value process that depends on its credit rating. Given
these extensions, our model is more flexible than the JLT model, and we are
clearly able to capture the above effect via numerical simulations. Furthermore,
from the perspective of practical implications, the JLT model tends to value
credit-linked coupon bonds more cheaply than does our model when the initial
credit rating is high, while the reverse is true for a low initial credit rating.
Keywords: risk management, derivative pricing, credit risk.
1 Introduction
The formulation and use of corporate bond valuation models dates from the work
of Merton [5]. In the Merton model, the default of a bond is defined as a state in
which the corporate value falls below the face amount of the bond, and in which
the corporate value process follows a geometric Brownian motion. As a result of
these assumptions, the Merton model may easily be used in conjunction with the
Black-Scholes formula to value corporate bonds. Using valuation frameworks of
this kind is typically characterised as following a \“structural approach,” and
Keywords
risk management, derivative pricing, credit risk.
Related Book
Other papers in this volume
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