Vulnerable American options

The purpose of this paper is to extend the models of Johnson and Stulz, Klein and Klein and lnglis to analyse the properties of vulnerable American options.

The presented model allows default prior to the maturity of the option based on a barrier which is linked to the payoff on the option. Various measures of risk denoted by the standard Greek letters are studied, as well as additional measures that arise because of the vulnerability.

The paper finds that the delta of a vulnerable American put does not always increase with the price of the underlying asset, and may be significantly smaller than that of a non‐vulnerable put. Because of deadweight costs associated with bankruptcy, delta and gamma are undefined for some values of the underlying asset. Rho may be considerably higher while vega may be smaller than for non‐vulnerable options. Also, the probability of early exercise for vulnerable American options is higher and the price of the underlying asset at which this is optimal depends on the degree of credit risk of the option writer.

This paper makes a contribution to understanding the effect of credit risk on option valuation.