A Note on the Black-Scholes Implied Volatility with Default Risk
Wilmott Journal, Vol. 2, No. 3, 2010
19 Pages Posted: 12 Nov 2008 Last revised: 14 Jun 2016
Date Written: November 10, 2008
This paper focuses on a theoretical aspect of relations between the Black-Scholes implied volatility and the default probability in a general framework that the stock price is fixed at zero after default occurs. It is shown that the default probability of the company under a risk-neutral measure significantly links to the implied volatility skew at extremely small strike. Moreover, it is proved that the divergence speed of the implied volatility must be determined uniquely in any defaultable economy under arbitrage-free condition. Finally, through a numerical test, we show whether our modelfree formula is applicable or not in practice.
Keywords: Implied Volatility, Default Probability, Arbitrage-Free Condition
JEL Classification: G13, G14, G33, C50
Suggested Citation: Suggested Citation