The Equity-Smile and Credit-Spread Puzzles: Are They One and the Same?

Abstract

We examine whether the puzzles of high prices for out-of-the-money put options on equity indices (the equity-smile puzzle) and large sizes of credit spreads on corporate bonds (the credit-spread puzzle) are related. To do this we compare the implied volatilities of long-term equity-index puts with the implied volatilities of puts within corporate bonds, at the bonds’ moneyness and maturity levels, in each month over 1992 to 2004. The data used are short-term index options, a proprietary set of long-term index options, and a set of zero-coupon bonds which are issued by investment companies. We find that the equity smile and the bond smile show remarkable similarity in all periods, not only in how volatility relates to moneyness but also in how it relates to maturity. This indicates that the same pricing kernel, with a high risk-premium on the extreme downside, is likely to explain them both.

Keywords: credit spread, implied volatility surface, volatility smile, pricing kernel, bond, equity-index option

JEL Classification: G12, G13