Jia-Wen Gu

On pricing basket credit default swaps

In this paper we propose a simple and efficient method to compute the ordered default time distributions in both the homogeneous case and the two-group heterogeneous case under the interacting intensity default contagion model. We give the analytical expressions for the ordered default time distributions with recursive formulas for the coefficients, which makes the calculation fast and efficient in finding rates of basket CDSs. In the homogeneous case, we explore the ordered default time in limiting case and further include the exponential decay and the multistate stochastic intensity process. The numerical study indicates that, in the valuation of the swap rates and their sensitivities with respect to underlying parameters, our proposed model outperforms the Monte Carlo method.

On Modeling Credit Defaults: A Probabilistic Boolean Network Approach

One of the central issues in credit risk measurement and management is modeling and predicting correlated defaults. In this paper we introduce a novel model to investigate the relationship between correlated defaults of different industrial sectors and business cycles as well as the impacts of business cycles on modeling and predicting correlated defaults using the Probabilistic Boolean Network (PBN). The key idea of the PBN is to decompose a transition probability matrix describing correlated defaults of different sectors into several BN matrices which contain information about business cycles. An efficient estimation method based on an entropy approach is used to estimate the model parameters. Using real default data, we build a PBN for explaining the default structure and making reasonably good predictions of joint defaults in different sectors.

Optimal Dividend Strategies of Two Collaborating Businesses in the Diffusion Approximation Model

In this paper, we consider the optimal dividend payment strategy for an insurance company that has two collaborating business lines. The surpluses of the business lines are modeled by diffusion processes. The collaboration between the two business lines permits that money can be transferred from one line to another with or without proportional transaction costs, while money must be transferred from one line to another to help both business lines keep running before simultaneous ruin of the two lines eventually occurs.

Optimal Portfolio Liquidation and Dynamic Mean-Variance Criterion

In this paper, we consider the optimal portfolio liquidation problem under the dynamic mean-variance criterion and derive time-consistent solutions in three important models. We give adapted optimal strategies under a reconsidered mean-variance subject at any point in time. We get explicit trading strategies in the basic model and when random pricing signals are incorporated. When we consider stochastic liquidity and volatility, we construct a generalized HJB equation under general assumptions for the parameters. We obtain an explicit solution in stochastic volatility model with a given structure supported by empirical studies.

A hidden Markov reduced-form risk model

In this paper, we propose a reduced-form credit risk model with a hidden state process. The hidden state process is adopted to model the underlying economic environment with an observable state revealing the delayed and noisy information of the underlying economic state. Our model is a generalization of the work in Gu et al. [1]. Under this framework, we give a computational method to extract the underlying economic state and to find the distribution of multiple default times. Numerical experiment is conducted to illustrate the impact of change in observable state and the contagion effect of defaults.

On Reduced Form Intensity-based Model with Trigger Events

Corporate defaults may be triggered by some major market news or events such as financial crises or collapses of major banks or financial institutions. With a view to develop a more realistic model for credit risk analysis, we introduce a new type of reduced-form intensity-based model that can incorporate the impacts of both observable ‘trigger’ events and economic environment on corporate defaults. The key idea of the model is to augment a Cox process with ‘trigger’ events. Both single-default and multiple-default cases are considered in this paper. In the former case, a simple expression for the distribution of the default time is obtained. Applications of the proposed model to price defaultable bonds and multi-name Credit Default Swaps are provided.

On Infectious Models for Dependent Default Risk

Modeling dependent defaults is a key issue in risk measurement and management. In this paper, we introduce a Markovian infectious model to describe the dependent relationship of default processes of credit entities. The key idea of the proposed model is based on the concept of common shocks adopted in the insurance industry. We compare the proposed model to both one-sector and two-sector models considered in the credit literature using real default data. A log-likelihood ratio test is applied to compare the goodness-of-fit of the proposed model. Our empirical results reveal that the proposed model outperforms both the one-sector and two-sector models.

On Infectious Model for Dependent Defaults

In this paper, we propose a two-sector Markovian infectious model, which is an extension of Greenwoods model. The central idea of this model is that the causality of defaults of two sectors is in both direction, which enrich dependence dynamics. The Bayesian Information Criterion is adopted to compare the proposed model with the two-sector model in credit literature using the real data. We find that the newly proposed model is statistically better than the model in past literature. We also introduce two measures: CRES and CRVaR to give risk evaluation of our model.