Credit Risk and Nonlinear Filtering : Computational Aspects and Empirical

This thesis proposes a novel credit risk model which deals with incomplete information on the firm’s asset value. Such incompleteness is due to reporting bias deliberately introduced by insider managers and executives of the firm and unobserved by outsiders. The pricing of corporate securities and the evaluation of default measures in our credit risk framework requires the solution of a computationally unfeasible nonlinear filtering problem. We propose a polynomial time-sequential Bayesian approximation scheme which employs convex optimization methods to iteratively approximate the optimal conditional density of the state on the basis of received market observations. We also provide an upper bound on the total variation distance between the actual filter density and our approximate estimator. We use the filter estimator to derive analytical expressions for the price of corporate securities (bond and equity) as well as for default measures (default probabilities, recovery rates, and credit spreads) under our credit risk framework. We propose a novel statistical calibration method to recover the parameters of our credit risk model from market price of equity and balance sheet indicators. We apply the method to the Parmalat case, a real case of misreporting and show that the model is able to successfully isolate the misreporting component. We also provide empirical evidence that the term structure of credit default swaps quotes exhibits special patterns in cases of misreporting by using three well known cases of accounting irregularities in US history: Tyco, Enron, and WorldCom. We conclude the thesis with a study of bilateral credit risk, which accommodates the case in which both parties of the financial contract may default on their payments. We introduce the general arbitrage-free valuation framework for counterparty risk adjustments in presence of bilateral default risk. We illustrate the symmetry in the valuation and show that the adjustment involves a long position in a put option plus a short position in a call option, both with zero strike and written on the residual net value of the contract at the relevant default times. We allow for correlation between the default times of each party of the contract and the underlying portfolio risk factors. We introduce stochastic intensity models and a trivariate copula function on the default times exponential variables to model default dependence. We provide evidence that both default correlation and credit spread volatilities have a relevant and structured impact on the adjustment. We also study a case involving British Airways, Lehman Brothers, and Royal Dutch Shell, illustrating the bilateral adjustments in concrete crisis situations.