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Abstract:
This paper proposes a method for constructing a volatility risk premium, or investor risk aversion, index. The method is intuitive and simple to implement, relying on the sample moments of the recently popularized model-free realized and option-implied volatility measures. A small-scale Monte Carlo experiment confirms that the procedure works well in practice. Implementing the procedure with actual S&P 500 option-implied volatilities and high-frequency five-minute-based realized volatilities indicates significant temporal dependencies in the estimated stochastic volatility risk premium, which we in turn relate to a set of macro-finance state variables. We also find that the extracted volatility risk premium helps predict future stock market returns.

Stochastic Volatility Risk Premium, Model-Free Implied Volatility, Model-Free Realized Volatility, Black-Scholes, GMM Estimation, Return Predictability

Abstract:
This paper proposes a method for constructing a volatility risk premium, or investor risk aversion, index. The method is intuitive and simple to implement, relying on the sample moments of the recently popularized model-free realized and option-implied volatility measures. A small-scale Monte Carlo experiment confirms that the procedure works well in practice. Implementing the procedure with actual S&P500 option-implied volatilities and high-frequency five-minute-based realized volatilities indicate significant temporal dependencies in the estimated stochastic volatility risk premium, which we in turn relate to a set of underlying macro-finance state variables. We also find that the extracted volatility risk premium helps predict future stock market returns.

Stochastic Volatility Risk Premium, Model-Free Implied Volatility, Model-Free Realized Volatility, Black-Scholes, GMM Estimation, Return Predictability

Abstract:
We find that the difference between implied and realized variances, or the variance risk premium, is able to explain more than fifteen percent of the ex-post time series variation in quarterly excess returns on the market portfolio over the 1990 to 2005 sample period, with high (low) premia predicting high (low) future returns. The magnitude of the return predictability of the variance risk premium easily dominates that afforded by standard predictor variables like the P/E ratio, the dividend yield, the default spread, and the consumption-wealth ratio (CAY). Moreover, combining the variance risk premium with the P/E ratio results in an R2 for the quarterly returns of more than twenty-five percent. The results depend crucially on the use of "model-free", as opposed to standard Black-Scholes, implied variances, and realized variances constructed from high-frequency intraday, as opposed to daily, data. Our findings suggest that temporal variation in risk and risk-aversion both play an important role in determining stock market returns.

Return Predictability, Implied Variance, Realized Variance, Equity Risk Premium, Variance Risk Premium, Time-Varying Risk Aversion

Abstract:
Motivated by the implications from a stylized self-contained general equilibrium model incorporating the effects of time-varying economic uncertainty, we show that the difference between implied and realized variation, or the variance risk premium, is able to explain a non-trivial fraction of the time series variation in post 1990 aggregate stock market returns, with high (low) premia predicting high (low) future returns. Our empirical results depend crucially on the use of "model-free,'' as opposed to Black-Scholes, options implied volatilities, along with accurate realized variation measures constructed from high-frequency intraday, as opposed to daily, data. The magnitude of the predictability is particularly strong at the intermediate quarterly return horizon, where it dominates that afforded by other popular predictor variables, like the P/E ratio, the default spread, and the consumption-wealth ratio (CAY).

Equilibrium asset pricing, stochastic volatility, risk neutral expectation, return predictability, option implied volatility, realized volatility, variance risk premium

Abstract:
This paper attempts to explain the credit default swap (CDS) premium, using a novel approach to identify the volatility and jump risks of individual firms from high-frequency equity prices. Our empirical results suggest that the volatility risk alone predicts 48 percent of the variation in CDS spread levels, whereas the jump risk alone forecasts 19 percent. After controlling for credit ratings, macroeconomic conditions, and firms' balance sheet information, we can explain 73 percent of the total variation. We calibrate a Merton-type structural model with stochastic volatility and jumps, which can help to match credit spreads after controlling for the historical default rates. Simulation evidence suggests that the high-frequency-based volatility measures can help to explain the credit spreads, above and beyond what is already captured by the true leverage ratio.

Credit Default Swap, Credit Risk Premium, Stochastic Volatility, Jumps, Structural Model, Nonlinear Effect, High-Frequency Data

Abstract:
This paper extends the jump detection method based on bipower variation to identify realized jumps on financial markets and to estimate parametrically the jump intensity, mean, and variance. Finite sample evidence suggests that the jump parameters can be accurately estimated and that the statistical inferences are reliable under the assumption that jumps are rare and large. Applications to equity market, treasury bond, and exchange rate data reveal important differences in jump frequencies and volatilities across asset classes over time. For investment grade bond spread indices, the estimated jump volatility has more forecasting power than interest rate factors and volatility factors including option-implied volatility, with control for systematic risk factors. The jump volatility risk factor seems to capture the low frequency movements in credit spreads and comoves counter cyclically with the price-dividend ratio and corporate default rate.

Jump-Diffusion Process, Realized Variance, Bi-Power Variation, Realized Jumps, Jump Volatility, Credit Risk Premium.

Abstract:
This paper provides a simple theoretical framework for assessing the empirical linkages between returns and realized and implied volatilities. First, we show that whereas the volatility feedback effect as measured by the sign of the correlation between contemporaneous return and realized volatility depends importantly on the underlying structural model parameters, the correlation between return and implied volatility is unambiguously positive for all reasonable parameter configurations. Second, the asymmetric response of current volatility to lagged negative and positive returns, typically referred to as the leverage effect, is always stronger for implied than realized volatility. Third, implied volatilities generally provide downward biased forecasts of subsequent realized volatilities. Our results help explain previous findings reported in the extant empirical literature, and is further corroborated by new estimation results for a sample of monthly returns and implied and realized volatilities for the S&P500 aggregate market index.

Leverage Asymmetry, Volatility Feedback, Implied Volatility Forecast, Realized Volatility, Stochastic Volatility Model, Instrument Variable

Abstract:
This paper provides a simple theoretical framework for assessing the empirical linkages between returns and realized and implied volatilities. First, we show that whereas the volatility feedback effect as measured by the sign of the correlation between contemporaneous return and realized volatility depends importantly on the underlying structural model parameters, the correlation between return and implied volatility is unambiguously positive for all reasonable parameter configurations. Second, the asymmetric response of current volatility to lagged negative and positive returns, typically referred to as the leverage effect, is always stronger for implied than realized volatility. Third, implied volatilities generally provide downward biased forecasts of subsequent realized volatilities. Our results help explain previous findings reported in the extant empirical literature, and is further corroborated by new estimation results for a sample of monthly returns and implied and realized volatilities for the S\&P500 aggregate market index.

Leverage Asymmetry, Volatility Feedback,Implied Volatility Forecast, Realized Volatility, Stochastic Volatility Model, Instrument Variable

Abstract:
We exploit the distributional information contained in high-frequency intraday data in constructing a simple conditional moment estimator for stochastic volatility diffusions. The estimator is based on the analytical solutions of the first two conditional moments for the latent integrated volatility, the realization of which is effectively approximated by the sum of the squared high-frequency increments of the process. Our simulation evidence indicates that the resulting GMM estimator is highly reliable and accurate. Our empirical implementation based on high-frequency five-minute foreign exchange returns suggests the presence of multiple latent stochastic volatility factors and possible jumps.

Stochastic volatility diffusions, integrated volatility, quadratic variation, realized volatility, high-frequency data, foreign exchange rates, GMM Estimation

Abstract:
This paper presents asset predictability evidence from the difference between implied and expected variances or variance risk premium that: (1) the variance difference measure predicts a significant positive risk premium across equity, bond, and credit markets; (2) the predictability is short-run, in that it peaks around one to four months and dies out as the horizon increases; and (3) such a short-run predictability is complementary to that of the standard predictor variables - P/E ratio, forward spread, and short rate. These findings are potentially justifiable by a general equilibrium model with recursive preference that incorporates stochastic economic uncertainty. Calibration evidence suggests that such a framework is capable of reproducing the variance premium dynamics, especially its high skewness and kurtosis, without introducing jumps. The calibrated model can also qualitatively explain the equity premium puzzle and the bond risk premia in short horizons.

Short-run predictability, variance premium dynamics, equity premium puzzle, bond risk premia, credit spread puzzle, macroeconomic uncertainty, recursive preference.

Abstract:
In this paper we propose a framework for measuring and stress testing the systemic risk for a group of major financial institutions. The systemic risk is measured by the price of insurance against financial distresses, which is based on ex ante measures of default probabilities of individual banks and forecasted asset return correlations. Importantly, using realized correlations estimated from high-frequency equity return data can significantly improve the accuracy of forecasted correlations. In addition, our stress testing methodology, as an integrated micro-macro model, takes into account dynamic linkages between the health of major US banks and the macro-financial condition. Our results suggest that the insurance premium to protect against losses that equal or exceed 15% of total liabilities of 12 major US financial firms stands at 110 billion in March 2008 and has a projected upper bound of 250 billion in July 2008.

Our methodology is closely related to but in sharp contrast with the Financial Stability Assessment Program (FSAP) conducted by IMF in recent years, the Supervisory Capital Assessment Program (SCAP) implemented by the U.S. regulatory authorities earlier this year, and the European-wide stress testing program sanctioned by the Committee of European Banking Supervisors (CEBS). These supervisory stress testing programs are primarily based on confidential banking information and adopt the historical stress scenarios as adverse as in the Great Depression era. In contrast, we rely on public banking information from the financial markets and use the statistical bootstrapping method to consistently assess the downside extreme outcomes. Therefore our approach is more applicable by the private sector in measuring and managing the systemic risk exposures of large complex banking institutions.

The concept of market-based stress testing and systemic risk assessment is an extension of the original idea by Merton and Perold (1993) that the capital of financial institutions is a risk-neutral concept reflected in current asset prices. A¨ıt-Sahalia and Lo (2000) regard value-at-risk (VaR) as inherently a risk-adjusted quantity implied by financial markets. A recent paper by Heaton, Lucas, and McDonald (2008) explicitly argues that capital reserve is a risk-neutral measurement.

Systemic risk, stress testing, portfolio credit risk, credit default swap, high-frequency data

Abstract:
We examine various dynamic term structure models for monthly US Treasury yields from 1964 to 2001. Of particular interest is the predictability of bond excess returns. Recent evidence indicates that using multiple forward rates can sharply predict future excess returns on bonds; the R2 of this predictability regression can be as high as 30%. In addition, the projection coefficients in these predictability regressions exhibit a tent shaped pattern that relates to the maturity of the forward rate. This dimension of the data in conjunction with the transition dynamics of bond yields (i.e., conditional volatility and cross-correlation of bond yields) poses an serious challenge to term structure models. In this paper we present and estimate a regime-shifts term structure model - our findings show that this model can account for all aspects of the predictability regression and the transition dynamics of yields. Alternative models, such as, affine factor models cannot account for these features of the data. We find that the regimes in the model are related to the NBER business cycle indicator.

Term Structure of Interest Rates, Yield Curve, Regime Switching, Risk Premium, Expectation Hypothesis, Business Cycle, Efficient Method of Moments, EMM

Abstract:
We examine various dynamic term structure models for monthly US Treasury yields from 1964 to 2001. Of particular interest is the predictability of bond excess returns. Recent evidence indicates that using multiple forward rates can sharply predict future excess returns on bonds; the R2 of this predictability regression can be as high as 30%. In addition, the projection coefficients in these predictability regressions exhibit a tent shaped pattern that relates to the maturity of the forward rate. This dimension of the data in conjunction with the transition dynamics of bond yields (i.e., conditional volatility and cross-correlation of bond yields) poses an serious challenge to term structure models. In this paper we present and estimate a regime-shifts term structure model - our findings show that this model can account for all aspects of the predictability regression and the transition dynamics of yields. Alternative models, such as, affine factor models cannot account for these features of the data. We find that the regimes in the model are related to the NBER business cycle indicator.

Term Structure of Interest Rates, Yield Curve, Regime Switching, Risk Premium, Expectation Hypothesis, Business Cycle, Efficient Method of Moments, EMM

Abstract:
In this paper we conduct a specification analysis of structural credit risk models, using term structure of credit default swap (CDS) spreads and equity volatility from high-frequency return data. Our study provides consistent econometric estimation of the pricing model parameters and specification tests based on the joint behavior of time-series asset dynamics and cross-sectional pricing errors. Our empirical tests reject strongly the standard Merton (1974) model, the Black and Cox (1976) barrier model, and the Longstaff and Schwartz (1995) model with stochastic interest rates. The double exponential jump-diffusion barrier model (Huang and Huang, 2003) improves significantly over the three models. The best one among the five models considered is the stationary leverage model of Collin-Dufresne and Goldstein (2001), which we cannot reject in more than half of our sample firms. However, our empirical results document the inability of the existing structural models to capture the dynamic behavior of CDS spreads and equity volatility, especially for investment grade names. This points to a potential role of time-varying asset volatility, a feature that is missing in the standard structural models.

Structural Credit Risk Models, Credit Default Swap Spreads, High Frequency Equity Volatility, Consistent Specification Analysis, Pricing Error Diagnostics

Abstract:
We find that augmenting a regression of excess bond returns on the term structure of forward rates with an estimate of the mean realized jump size almost doubles the R2 of the forecasting regression. The return predictability from augmenting with the jump mean easily dominates that offered by augmenting with options-implied volatility and realized volatility from high frequency data. In out-of-sample forecasting exercises, inclusion of the jump mean can reduce the root mean square prediction error by up to 40 percent. The incremental return predictability captured by the realized jump mean largely accounts for the countercyclical movements in bond risk premia. This result is consistent with the setting of an incomplete market in which the conditional distribution of excess bond returns is affected by a jump risk factor that does not lie in the span of the term structure of yields.

Unspanned Stochastic Volatility, Regime-Shift Term Structure, Bond Return Predictability, Expectations Hypothesis, Countercyclical Risk Premia, Realized Jump Risk

Abstract:
We develop a term structure model where the short interest rate and the market price of risks are subject to discrete regime shifts. Empirical evidence from Efficient Method of Moments estimation provides considerable support for the regime shifts model. Standard models, which include affine specifications with up to three factors, are sharply rejected in the data. Our diagnostics show that only the regime shifts model can account for the well documented violations of the expectations hypothesis, the observed conditional volatility, and the conditional correlation across yields. We find that regimes are intimately related to business cycles.

Abstract:
We develop a term structure model where the short interest rate and the market price of risks are subject to discrete regime shifts. Empirical evidence from Efficient Method of Moments estimation provides considerable support for the regime shifts model. Standard models, which include affine specifications with up to three factors, are sharply rejected in the data. Our diagnostics show that only the regime shifts model can account for the well documented violations of the expectations hypothesis, the observed conditional volatility, and the conditional correlation across yields. We find that regimes are intimately related to business cycles.

Regime switching, term structure of interest rate, reprojection, efficient method of moments

Abstract:
This paper performs a Monte Carlo study on Efficient Method of Moments (EMM), Generalized Method of Moments (GMM), Quasi-Maximum Likelihood Estimation (QMLE), and Maximum Likelihood Estimation (MLE) for a continuous-time square-root model under two challenging scenarios/high persistence in mean and strong conditional volatility/that are commonly found in estimating the interest rate process. MLE turns out to be the most efficient of the four methods, but its finite sample inference and convergence rate suffer severely from approximating the likelihood function, especially in the scenario of highly persistent mean. QMLE comes second in terms of estimation efficiency, but it is the most reliable in generating inferences. GMM with lag-augmented moments has overall the lowest estimation efficiency, possibly due to the ad hoc choice of moment conditions. EMM shows an accelerated convergence rate in the high volatility scenario, while its overrejection bias in the mean persistence scenario is unacceptably large. Finally, under a stylized alternative model of the US interest rates, the overidentification test of EMM obtains the ultimate power for detecting misspecification, while the GMM J-test is increasingly biased downward in finite samples.

Monte Carlo Study, Efficient Method of Moments, Maximum Likelihood Estimation, Square-Root Diffusion, Quasi-Maximum Likelihood, Generalized Method of Moments

Abstract:
This paper implements a Multivariate Weighted Nonlinear Least Square estimator for a class of jump-diffusion interest rate processes (hereafter MWNLS-JD), which also admit closed-form solutions to bond prices under a no-arbitrage argument. The instantaneous interest rate is modeled as a mixture of a square-root diffusion process and a Poisson jump process. One can derive analytically the first four conditional moments, which form the basis of the MWNLS-JD estimator. A diagnostic conditional moment test can also be constructed from the fitted moment conditions. The market prices of diffusion and jump risks are calibrated by minimizing the pricing errors between a model-implied yield curve and a target yield curve. The time series estimation of the short-term interest rate suggests that the jump augmentation is highly significant and that the pure diffusion process is strongly rejected. The cross-sectional evidence indicates that the jump-diffusion yield curves are both more flexible in reducing pricing errors and are more consistent with the Martingale pricing principle.

Jump-diffusion, term structure of interest rates, conditional moment generator, multivariate weighted nonlinear least square, market price of risk

Abstract:
We estimate the nondefault component of corporate bond yield spreads and examine its relationship with bond liquidity. We measure bond liquidity using intraday transactions data and estimate the default component using the term structure of credit default swaps (CDS) spreads. With swap rate as the risk free rate, the estimated nondefault component is generally moderate but statistically significant for AA-, A-, and BBB-rated bonds and increasing in this order. With Treasury rate as the risk free rate, the estimated nondefault component is the largest in basis points for BBB-rated bonds but as a fraction of yield spreads for AAA-rated bonds. Controlling for the unobservable firm heterogeneity, we find a positive and significant relationship between the nondefault component and illiquidity for investment-grade bonds but no significant relationship for speculative-grade bonds. We also find that the nondefault component comoves with macroeconomic conditions - negatively with the Treasury term structure and positively with the stock market implied volatility.

Corporate bond yields, credit default swaps, liquidity

Abstract:
We find that variance risk premia, defined as the spread between the option-implied and expected variances, have a prominent predictability for the credit default swap spreads at individual firm level. Such a predictability cannot be crowded out by that of the market and firm level credit risk factors identified in previous research. We demonstrate that the strong predictability of implied variance for credit spreads is mostly explained by either variance premium or expected variance. Our findings suggest that variance risk premium is a relatively clean measure of a firm’s exposure to macroeconomic uncertainty or systematic variance risk, while option-implied variance may be contaminated by idiosyncratic variance risk. Such a result is consistent with the market level evidence that variance risk premium predicts credit spread variation.

variance risk premia, credit default swap spreads, option-implied variance, expected variance, realized variance

Abstract:
This paper extends the approach of measuring and stress-testing the systemic risk of a banking sector in Huang, Zhou, and Zhu (2009) to identifying various sources of financial instability and to allocating systemic risk to individual financial institutions. The systemic risk measure, defined as the insurance cost to protect against distressed losses in a banking system, is a risk-neutral concept of capital based on publicly available information that can be appropriately aggregated across different subsets. An application of our methodology to a portfolio of twenty-two major banks in Asia and the Pacific illustrates the dynamics of the spillover effects of the global financial crisis to the region. The increase in the perceived systemic risk, particularly after the failure of Lehman Brothers, was mainly driven by the heightened risk aversion and the squeezed liquidity. The analysis on the marginal contribution of individual banks to the systemic risk suggests that “too-big-to-fail” is a valid concern from a macroprudential perspective of bank regulation.

Systemic risk, Macroprudential regulation, Portfolio distress loss, Credit default swap, Dynamic conditional correlation

Abstract:
This article exploits the Ito's formula to derive the conditional moments vector for the class of interest rate models that allow for nonlinear volatility and flexible jump specifications. Such a characterization of continuous-time processes by the Ito conditional moment generator noticeably enlarges the admissible set beyond the affine jump-diffusion class. A simple generalized method of moments (GMM) estimator can be constructed based on the analytical solution to the lower-order moments, with natural diagnostics of the conditional mean, variance, skewness, and kurtosis. Monte Carlo evidence suggests that the proposed estimator has desirable finite sample properties relative to the asymptotically efficient maximum - likelihood estimator (MLE). The empirical application singles out the nonlinear quadratic variance as the key feature of the U.S. short-rate dynamics.

Ito conditional moment generator , quadratic variance, jump-diffusion process, generalized method of moments, Monte-Carlo study

Abstract:
This paper attempts to explain the credit default swap (CDS) premium, using a novel approach to identify the volatility and jump risks of individual firms from high-frequency equity prices. Our empirical results suggest that the volatility risk alone predicts 48% of the variation in CDS spread levels, whereas the jump risk alone forecasts 19%. After controlling for credit ratings, macroeconomic conditions, and firms' balance sheet information, we can explain 73% of the total variation. We calibrate a Merton-type structural model with stochastic volatility and jumps, which can help to match credit spreads after controlling for the historical default rates. Simulation evidence suggests that the high-frequency-based volatility measures can help to explain the credit spreads, above and beyond what is already captured by the true leverage ratio.

G12, G13, C14

Abstract:
In this paper we propose a framework for measuring and stress testing the systemic risk for a group of major commercial banks and investment banks. The systemic risk is measured by the price of insurance against financial distresses, which is based on ex ante measures of default probabilities of individual banks and forecasted asset return correlations. Importantly, using realized correlations estimated from high-frequency equity return data can significantly improve the accuracy of forecasted correlations. In addition, our stress testing methodology, as an integrated micro-macro model, takes into account dynamic linkages between the health of major US banks and the macro-financial condition.

This paper is currently reserved to Carefin sponsors and will be made public on SSRN after a short embargo. Please visit the CAREFIN website to learn more on how to get the paper.

Stress testing, systemic risk, insurance premium, default probability, credit default swap spread, high-frequency data, asset return correlation