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Working Paper
Expectations of functions of stochastic time with application to credit risk modeling
We develop two novel approaches to solving for the Laplace transform of a time-changed stochastic process. We discard the standard assumption that the background process (Xt) is Levy. Maintaining the assumption that the business clock (Tt) and the background process are independent, we develop two different series solutions for the Laplace transform of the time-changed process X-tildet=X(Tt). In fact, our methods apply not only to Laplace transforms, but more generically to expectations of smooth functions of random time. We apply the methods to introduce stochastic time change to the ...
Working Paper
The information content of high-frequency data for estimating equity return models and forecasting risk
We demonstrate that the parameters controlling skewness and kurtosis in popular equity return models estimated at daily frequency can be obtained almost as precisely as if volatility is observable by simply incorporating the strong information content of realized volatility measures extracted from high-frequency data. For this purpose, we introduce asymptotically exact volatility measurement equations in state space form and propose a Bayesian estimation approach. Our highly efficient estimates lead in turn to substantial gains for forecasting various risk measures at horizons ranging from a ...
Working Paper
The information content of high-frequency data for estimating equity return models and forecasting risk
We demonstrate that the parameters controlling skewness and kurtosis in popular equity return models estimated at daily frequency can be obtained almost as precisely as if volatility is observable by simply incorporating the strong information content of realized volatility measures extracted from high-frequency data. For this purpose, we introduce asymptotically exact volatility measurement equations in state space form and propose a Bayesian estimation approach. Our highly efficient estimates lead in turn to substantial gains for forecasting various risk measures at horizons ranging from a ...
Working Paper
An Evaluation of Bank VaR Measures for Market Risk During and Before the Financial Crisis
We study the performance and behavior of Value at Risk (VaR) measures used by a number of large banks during and before the financial crisis. Alternative benchmark VaR measures, including GARCH-based measures, are also estimated directly from the banks' trading revenues and help to explain the bank VaR performance results. While highly conservative in the pre-crisis period, bank VaR exceedances were excessive and clustered in the crisis period. All benchmark VaRs were more accurate in the pre-crisis period with GARCH VaR measures the most accurate in the crisis period having lower exceedance ...
Working Paper
Bayesian Estimation of Time-Changed Default Intensity Models
We estimate a reduced-form model of credit risk that incorporates stochastic volatility in default intensity via stochastic time-change. Our Bayesian MCMC estimation method overcomes nonlinearity in the measurement equation and state-dependent volatility in the state equation. We implement on firm-level time-series of CDS spreads, and find strong in-sample evidence of stochastic volatility in this market. Relative to the widely-used CIR model for the default intensity, we find that stochastic time-change offers modest benefit in fitting the cross-section of CDS spreads at each point in time, ...
Working Paper
Bayesian analysis of stochastic volatility models with Lévy jumps: application to risk analysis
In this paper I analyze a broad class of continuous-time jump diffusion models of asset returns. In the models, stochastic volatility can arise either from a diffusion part, or a jump part, or both. The jump component includes either compound Poisson or Lvy alpha-stable jumps. To be able to estimate the models with latent Lvy alpha-stable jumps, I construct a new Markov chain Monte Carlo algorithm. I estimate all model specifications with S&P500 daily returns. I find that models with Levy alpha-stable jumps perform well in capturing return characteristics if diffusion is a source of ...