HAYETTE GATFAOUI 109risk is mainly driven by idiosyncratic risk (Campbell and Taksler, 2003).
Though market variance has no predictive power for market return, a sig-
nificant positive relationship prevails between average stock variance and
market return. Finally, Stein, Kocagil, Bohn and Akhavein (2003) analyze
default risk in the lens of idiosyncratic and systematic risk. Given their
results, idiosyncratic information is mostly important for predicting middle
market defaults.
Documented research has shed light on the typology and components
of credit risk. Given the state of the art, credit risk has to be envisioned
along with two dimensions, namely systematic and idiosyncratic risk. Such
a typology is used by Gatfaoui (2003) to price risky debt in a Merton (1974)
framework where diffusion parameters are constant. However, under its
constant parameter assumption, Merton’s model leads to implied spreads,
which are far below observed credit spreads. Indeed, Eom, Helwege, and
Huang (2004) show that adding stochastic interest rates correlated with
firm value in Merton’s model fails to offset the implied credit spreads’ pre-
diction problem. To solve this problem, Hull, Nelken, and White (2003)
study the implications of Merton’s model regarding implied at-the-money
volatility and volatility skews. Their findings are supported by empirical
data. First, implied volatility is sufficient to predict credit spreads. Second,
there is a positive relationship between credit spreads and implied volatility,
and between volatility skews and both implied credit spreads and implied
volatility.
Third, implied volatility plays a major role in explaining credit spreads.
Finally, as historical volatility leads to implied credit spreads, which
underestimate their observed counterparts, the implied volatility approach
exhibits a superior performance in predicting credit spreads over time. Such
findings are consistent with Black and Scholes (1973) option pricing-type
models. Specifically, such models exhibit a volatility smile (for exam-
ple, implied volatility is a U-shaped function of the option’s moneyness),
which is determined by stochastic volatility, maturity and systematic risk
among others (see Äijö, 2003; Backus, Foresi, Li and Wu, 1997; Duque
and Lopes, 2003 for details, and Psychoyios, Skiadopoulos and Alexakis,
2003, for a survey about stylized facts of volatility as well as stochastic
volatility models). Moreover, Eberlein, Kallsen and Kristen (2002/2003)
study different representations of asset returns’ volatility. They consider
successively a constant parameter, a non-parametric model, a GARCH
model, an autoregressive exponential model, a composite model,^1 and
finally a stochastic volatility diffusion model generating an implied volatil-
ity. Their classification according to Basel rules^2 shows that first implied
volatility models, and second GARCH-type models perform much bet-
ter than other volatility representations in terms of Value-at-Risk forecasts
(for example, frequency of excessive losses that determines required capital
reserves).