Estimation of Stable distribution and Its Application to Credit Risk

To capture the heavy tails and the volatility clustering of asset returns is always an important topic in financial market. We studies two projects related to the Alpha Stable distribution and Classical Tempered Stable(CTS) distribution respectively which both have desired properties to accommodate heavy-tails and capture skewness in financial series. (1) In the major part of the first project, we introduce the algorithm of indirect inference method. By using the skewed-t distribution as an auxiliary model which is easier to handle, we can estimate the parameters of the Alpha Stable distribution since these two models have the same numbers of parameters and each of them plays a similar role. We also estimate of the parameters of the alpha stable distribution with McColloch method, Characteristic Function Based method and MLE method respectively. Finally, we provide an empirical application on S&P 500 returns and make comparisons between these four methods. (2) In the second project, we discuss the Gaussian firm value model and the Classical Tempered Stable firm value model. By pointing out the drawbacks of application of Merton's model on firm value, we introduce the classical tempered stable distribution and make the market firm value process follows a CTS distribution instead of Gaussian distribution. We estimate the parameters of the CTS, and calculate the firm value and default probability. By comparing these two models, the results suggest that CTS firm value model has a better potential to predict the default probability of a firm since it can better capture the heavy tails of the asset returns.