Default Risk in Stochastic Volatility Models - Hans Gersbach; Nicolae Surulescu (ETH Zurich, CER-ETH - Center of Economic Research, 2010)
We consider a stochastic volatility model of the mean-reverting type to describe the evolution of a firm's values instead of the classical approach by Merton with geometric Brownian motions. We develop an analytical expression for the default probability. Our simulation results indicate that the stochastic volatility model tends to predict higher default probabilities than the corresponding Merton model if a firm's credit quality is not too low. Otherwise the stochastic volatility model predicts lower probabilities of default. The results may have implications for various financial applications.
Keywords: G13; G21; G32; 330; stochastic volatility; Merton model; default probabilities; rate of mean reversion; Optionspreistheorie; Kapitaleinkommen; Volatilität; Stochastischer Prozess; Mean Reversion; Theorie