Understanding the Default-Implied Volatility for Credit Spreads

by Changguang K. Zheng of Morgan Stanley Dean Witter

April 1999

Abstract: This paper presents a simple reduce-form approach to pricing credit derivatives.  The definition of default is purely based on the market value of a risky bond and its potential recovery value.  A risky bond is treated as a riskless bond with an embedded short position on a barrier option.  The risky bond market implicitly prices this barrier option.  The default implied volatility (DIV) curve for credit spread is derived from the values of barrier options.  The DIV curve is useful for pricing volatility-sensitive credit derivatives.  In this paper, we show how the DIV curve is used to consistently price a credit spread put option and a first-to-default swap.  The correlation matrix of reference entities' credit spreads (not default arrival times) is used for pricing a first-to-default swap.

Published in: Journal of Derivatives, Vol. 7, No. 4, (Summer 2000), pp. 67-77.

Previously titled: Default Implied Volatility for Credit Spread