HAYETTE GATFAOUI 127we obtain an asymptotically mean reverting stochastic volatility process
relative to time. Moreover, an interesting implication of our model is
the stochastic correlation coefficient prevailing between firm value and its
idiosyncratic risk factor. We study this dependence feature as well as the
stochastic volatility process through simulations. Specifically, accelerator-
based Monte Carlo simulations are undertaken to study the behaviors of
equity, debt and credit spreads as functions of our model’s parameters. In
the same way, we also simulated the path-dependent average stochastic
volatility of our pricing framework. The advantage of such a setting is the
flexibility given by parameters since we are able to account for many risk
scenarios and various market-linked firms. Moreover, the boundedness of
firm value’s stochastic volatility implies the boundedness of related equity,
debt and credit spreads. Such bounds can be viewed as extreme scenar-
ios (worst/minimal potential losses due to increased/reduced global risk
where the level of firm’s global risk depends on systematic and idiosyncratic
risk factors). In particular, our stochastic setting can allow for a more accu-
rate computation of historical conditional default probabilities. As default
probabilities allows for assessing creditworthiness of counterparts, the pos-
sible boundedness of such probabilities given likely scenarios has some
non-negligible importance and significance.
Our paper presents then some non-negligible advantages. First, volatility
is fundamental for asset valuation, risk management and portfolio diver-
sification (Eberlein, Kallsen and Kristen, 2002/2003). Stochastic volatility
models are useful tools to account for fundamental time-varying volatility
(latent volatility component) of financial assets (Hwang and Satchell, 2000).
Moreover, volatility is commonly thought as a liquidity indicator (Kerpoff,
1987; Lamoureux and Lastrapes, 1990; Schwert, 1989). Hence, incorporating
a stochastic volatility in credit risk modeling implicitly accounts for some
liquidity effects describing credit risky assets (Collin-Dufresne, Goldstein
and Martin, 2001; Delianedis and Geske, 2001). Incidentally, Ericsson and
Renault (2003) show that credit spreads encompass a liquidity premium,
which is an increasing function of firm value, leverage and aggregate volatil-
ity. Therefore, stochastic volatility will help accounting for a widening of
credit spreads due to an increase in the liquidity premium they encompass
(Cunningham, Dixon and Hayes, 2001, regarding sovereign bonds). Finally,
the stochastic aggregate volatility we obtain is the result of our stochastic
functionals’ combination. Thus, the flexibility offered by possible specifica-
tions of such functionals allows considering investment grade debt and part
of speculative grade debt.
On the other hand, our credit pricing model is equivalent to a stochastic
volatility Merton-type pricing model, which is valuable. Indeed, Kealhofer
and Kurbat (2001) show that Merton’s approach outperforms both Moody’s
credit ratings and well-known accounting ratios in predicting default. The
Merton-type approach contains any information embedded in such ratings