Junye Li

Self-exciting jumps, learning, and asset pricing implications

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.The paper proposes a self-exciting asset pricing model that takes into account co-jumps between prices and volatility and self-exciting jump clustering. We employ a Bayesian learning approach to implement real time sequential analysis. We find evidence of self-exciting jump clustering since the 1987 market crash, and its importance becomes more obvious at the onset of the 2008 global financial crisis. It is found that learning affects the tail behaviors of the return distributions and has important implications for risk management, volatility forecasting and option pricing.

Efficient Learning via Simulation: A Marginalized Resample-Move Approach

In state-space models, parameter learning is practically dicult and is still an open issue. This paper proposes an ecient simulation-based parameter learning method. First, the approach breaks up the interdependence of the hidden states and the static parameters by marginalizing out the states using a particle lter. Second, it applies a Bayesian resample-move approach to this marginalized system. The methodology is generic and needs little design eort. Dierent from batch estimation methods, it provides posterior quantities necessary for full sequential inference and recursive model monitoring. The algorithm is implemented both on simulated data in a linear Gaussian model for illustration and comparison and on real data in a L evy jump stochastic volatility model and a structural credit risk model.

An unscented Kalman smoother for volatility extraction: Evidence from stock prices and options

A smoothing algorithm based on the unscented transformation is proposed for the nonlinear Gaussian system. The algorithm first implements a forward unscented Kalman filter and then evokes a separate backward smoothing pass by only making Gaussian approximations in the state but not in the observation space. The method is applied to volatility extraction in a diffusion option pricing model. Both simulation study and empirical applications with the Heston stochastic volatility model indicate that in order to accurately capture the volatility dynamics, both stock prices and options are necessary.

A spectral estimation of tempered stable stochastic volatility models and option pricing

A characteristic function-based method is proposed to estimate the time-changed Levy models, which take into account both stochastic volatility and infinite-activity jumps. The method facilitates computation and overcomes problems related to the discretization error and to the non-tractable probability density. Estimation results and option pricing performance indicate that the infinite-activity model performs better than the finite-activity one. By introducing a jump component in the volatility process, a double-jump model is also investigated.

Sequential Bayesian Analysis of Time-Changed Infinite Activity Derivatives Pricing Models

This article investigates time-changed infinite activity derivatives pricing models from the sequential Bayesian perspective. It proposes a sequential Monte Carlo method with the proposal density generated by the unscented Kalman filter. This approach overcomes to a large extent the particle impoverishment problem inherent to the conventional particle filter. Simulation study and real applications indicate that (1) using the underlying alone cannot capture the dynamics of states, and by including options, the precision of state filtering is dramatically improved; (2) the proposed method performs better and is more robust than the conventional one; and (3) joint identification of the diffusion, stochastic volatility, and jumps can be achieved using both the underlying data and the options data.

Option-implied volatility factors and the cross-section of market risk premia

The main goal of this paper is to study the cross-sectional pricing of market volatility. The paper proposes that the market return, diffusion volatility, and jump volatility are fundamental factors that change the investors’ investment opportunity set. Based on estimates of diffusion and jump volatility factors using an enriched dataset including S&P 500 index returns, index options, and VIX, the paper finds negative market prices for volatility factors in the cross-section of stock returns. The findings are consistent with risk-based interpretations of value and size premia and indicate that the value effect is mainly related to the persistent diffusion volatility factor, whereas the size effect is associated with both the diffusion volatility factor and the jump volatility factor. The paper also finds that the use of market index data alone may yield counter-intuitive results.

The Variance Risk Premium: Components, Term Structures, and Stock Return Predictability

This article examines the properties of the variance risk premium (VRP). We propose a flexible asset pricing model that captures co-jumps in prices and volatility, and self-exciting jump clustering. We estimate the model on equity returns and variance swap rates at different horizons. The total VRP is negative and has a downward-sloping term structure, while its jump component displays an upward-sloping term structure. The abrupt and persistent response of the short-term jump VRP to extreme events makes this specific premium a proxy for investors’ fear of a market crash. Furthermore, the use of the VRP level and slope, and of its components, helps improve the short-run predictability of equity excess returns.

On Bank Credit Risk: Systemic or Bank Specific? Evidence for the United States and United Kingdom

We develop a multivariate credit risk model that accounts for joint defaults of banks and allows us to disentangle how much of banks’ credit risk is systemic. We find that the United States and United Kingdom differ not only in the evolution of systemic risk but, in particular, in their banks’ systemic exposures. In both countries, however, systemic credit risk varies substantially, represents about half of total bank credit risk on average, and induces high risk premia. The results suggest that sovereign and bank systemic risk are particularly interlinked in the United Kingdom.

Real-Time Bayesian Learning and Bond Return Predictability

The paper examines statistical and economic evidence of out-of-sample bond return predictability for a real-time Bayesian investor who learns about parameters, hidden states, and predictive models over time. We find some statistical evidence using information contained in forward rates. However, such statistical predictability can hardly generate any economic value for investors. Furthermore, we find that strong statistical and economic evidence of bond return predictability from fully-revised macroeconomic data vanishes when real-time macroeconomic information is used. We also show that highly levered investments in bonds can improve short-run bond return predictability.

Inferring Volatility Dynamics Using Stock Prices and Variance Swap Rates: An Efficient Bayesian Approach

In dynamic asset pricing models, when the model structure becomes complex and derivatives data are introduced in estimation, traditional Bayesian MCMC methods converge slowly, are difficult to design efficient proposals for parameters, and have large computational cost. We propose a two-stage sequential Monte Carlo sampler based on common random numbers and a smooth particle filter. This method is robust to potential model misspecification and can deliver almost full-likelihood-based inference at a much smaller computational cost. It is applied to estimate a class of volatility models that take into account price-volatility co-jumps, non-affineness, and self-excitation. An empirical study using S&P 500 index and variance swap rates shows that both non-affineness and self-excitation need to be introduced in modeling volatility dynamics.