q-Gaussian Model of Default : Valuation of CDS Spreads

The q-Gaussian generalization of the Merton framework allows pricing of the additional risk premium related to fluctuations of the variance of the market value of a company's assets, which can explain the observed level of short-term CDS spreads of investment grade issuers. The derived simple formula for a term-structure of CDS spreads depends on i) the risk neutral recovery rate, ii) the generalized Merton “distance to default”, and iii) the Tsallis entropic parameter q. For q=1, related to the sharply pointed distribution of variance and the normal Boltzmann-Gibbs-Shannon statistics, the derived formula reduces to the well-known result. We demonstrate that q-statistic, corresponding to q > 1, straightforwardly accounts for the variance risk, which leads to much higher short-term CDS spreads, which are severely undervalued by conventional structural models of default. An empirical application suggests that the derived expression allows closely matching the entire term-structure of the observed CDS spreads of the Boing Co. during relatively ‘calm' market periods