Estimating the Structural Credit Risk Model When Equity Prices Are Contaminated by Trading Noises

The transformed-data maximum likelihood estimation (MLE) method for structural credit risk models developed by Duan (1994) is extended to account for the fact that observed equity prices may have been contaminated by trading noises. With the presence of trading noises, the likelihood function based on the observed equity prices can only be evaluated via some nonlinear filtering scheme. We devise a particle filtering algorithm that is practical for conducting the MLE estimation of the structural credit risk model of Merton (1974). We implement the method on the Dow Jones 30 firms and on 100 randomly selected firms, and find that ignoring trading noises can lead to significantly over-estimating the firm’s asset volatility. The estimated magnitude of trading noise is in line with the direction that a firm’s liquidity will predict based on three common liquidity proxies. A simulation study is then conducted to ascertain the performance of the estimation method.Credit Risk; Maximum Likelihood; Microstructure; Option Pricing; Particle Filtering

Estimating the Structural Credit Risk Model When Equity Prices Are Contaminated by Trading Noises

The transformed-data maximum likelihood estimation (MLE) method for struc- tural credit risk models developed by Duan (1994) is extended to account for the fact that observed equity prices may have been contaminated by trading noises. With the presence of trading noises, the likelihood function based on the observed equity prices can only be evaluated via some nonlinear filtering scheme. We devise a particle filtering algorithm that is practical for conducting the MLE estimation of the structural credit risk model of Merton (1974). We implement the method on the Dow Jones 30 firms and on 100 randomly selected firms, and find that ignoring trading noises can lead to significantly over-estimating the firm's asset volatility. A simulation study is then conducted to ascertain the performance of the estimation method.Particle filtering, maximum likelihood, option pricing, credit risk, simulation

Feedback Effects of Rating Downgrades

This paper addresses whether credit rating downgrades feed back on the asset value of the downgraded companies, causing real losses. To investigate this issue we construct a structural credit risk model incorporating ratings and the feedback loss. To estimate the parameters of the model we develop a maximum likelihood estimator using time series of equity prices and credit ratings. Implementing the model on a sample of US public firms downgraded from investment grade to junk, we find strong support for the existence of feedback losses. First, estimated feedback losses are significant for a third of our sample with the cross-sectional averages of the feedback loss around 7 %. Second, the behavior of estimated asset volatilities around downgrades in real data is consistent with the predictions of our model. We observe a hump-shaped pattern of estimated asset volatilities when feedback is ignored. Using the feedback model, the hump-shaped pattern disappears. These findings suggest that ignoring feedback can lead to the appearance of changing asset volatility even when the real volatility is constant. Last, accounting for feedback helps in asset volatility prediction.Credit Ratings; Credit Risk; Distress Costs; Maximum Likelihood; Option Pricing

Bayesian Learning of Impacts of Self-Exciting Jumps in Returns and Volatility

The paper proposes a new class of continuous-time asset pricing models where negative jumps play a crucial role. Whenever there is a negative jump in asset returns, it is simultaneously passed on to diffusion variance and the jump intensity, generating self-exciting co-jumps of prices and volatility and jump clustering. To properly deal with parameter uncertainty and in-sample over-fitting, a Bayesian learning approach combined with an efficient particle filter is employed. It not only allows for comparison of both nested and non-nested models, but also generates all quantities necessary for sequential model analysis. Empirical investigation using S&P 500 index returns shows that volatility jumps at the same time as negative jumps in asset returns mainly through jumps in diffusion volatility. We find substantial evidence for jump clustering, in particular, after the recent financial crisis in 2008, even though parameters driving dynamics of the jump intensity remain difficult to identify.Self-Excitation, Volatility Jump, Jump Clustering, Extreme Events, Parameter Learning, Particle Filters, Sequential Bayes Factor, Risk Management

Bayesian Analysis of Bubbles in Asset Prices

Singapore MOE Academic Research Fund Tier 2Published in Econometrics https://doi.org/10.3390/econometrics5040047</p

Bayesian analysis of bubbles in asset prices

Ministry of Education, Singapore under its Academic Research Funding Tier

Estimating and Testing Long-Run Risk Models: International Evidence

We estimate and test long-run risk models using international macroeconomic and financial data. The benchmark model features a representative agent who has recursive preferences with a time preference shock, a persistent component in expected consumption growth, and stochastic volatility in fundamentals characterized by an autoregressive Gamma process. We construct a comprehensive dataset with quarterly frequency for ten developed countries and employ an efficient likelihood-based Bayesian method that exploits up-to-date sequential Monte Carlo methods to make full econometric inference. Our empirical findings provide international evidence in support of long-run risks, time-varying preference shocks, and countercyclicality of the stochastic discount factor. We show the existence of a global long-run consumption factor driving equity returns across individual countries

Self-Exciting Jumps, Learning, and Asset Pricing Implications

Published in Review of Financial Studies https://doi.org/10.1093/rfs/hhu078</p

Bayesian Learning of Impacts of Self-Exciting Jumps in Returns and Volatility

The paper proposes a new class of continuous-time asset pricing models where negative jumps play a crucial role. Whenever there is a negative jump in asset returns, it is simultaneously passed on to diffusion variance and the jump intensity, generating self-exciting co-jumps of prices and volatility and jump clustering. To properly deal with parameter uncertainty and in-sample over-fitting, a Bayesian learning approach combined with an efficient particle filter is employed. It not only allows for comparison of both nested and non-nested models, but also generates all quantities necessary for sequential model analysis. Empirical investigation using S&amp;P 500 index returns shows that volatility jumps at the same time as negative jumps in asset returns mainly through jumps in diffusion volatility. We find substantial evidence for jump clustering, in particular, after the recent financial crisis in 2008, even though parameters driving dynamics of the jump intensit

Estimating and Testing Long-Run Risk Models: International Evidence

We estimate and test long-run risk models using international macroeconomic and financial data. The benchmark model features a representative agent who has recursive preferences with a time preference shock, a persistent component in expected consumption growth, and stochastic volatility in fundamentals characterized by an autoregressive gamma process. We construct a comprehensive data set with quarterly frequency for 10 developed countries and employ an efficient likelihood-based Bayesian method that exploits up-to-date sequential Monte Carlo methods to make full econometric inference. Our empirical findings provide international evidence in support of long-run risks, time-varying preference shocks, and countercyclicality of the stochastic discount factor. We show the existence of a global long-run consumption factor driving equity returns across individual countries