Extracting Latent States from High Frequency Option Prices
We propose the realized option variance as a new observable variable to integrate high frequency option prices in the inference of option pricing models. Using simulation and empirical studies, this paper documents the incremental information offered by this realized measure. Our empirical results show that the information contained in the realized option variance improves the inference of model variables such as the instantaneous variance and variance jumps of the S&P 500 index. Parameter estimates indicate that the risk premium breakdown between jump and diffusive risks is affected by the omission of this information.
No Such Thing as Missing Data
The phrase "missing data" has come to mean "information we really, really wish we had". But is it actually data, and is it actually missing? I will discuss the practical implications of taking a different philosophical perspective, and demonstrate the use of a simple model for informative observation in longitudinal studies that does not require any notion of missing data.
Model Confidence Bounds for Variable Selection
In this article, we introduce the concept of model confidence bounds (MCBs) for variable selection in the context of nested models. Similarly to the endpoints in the familiar confidence interval for parameter estimation, the MCBs identify two nested models (upper and lower confidence bound models) containing the true model at a given level of confidence. Instead of trusting a single selected model obtained from a given model selection method, the MCBs proposes a group of nested models as candidates and the MCBs’ width and composition enable the practitioner to assess the overall model selection uncertainty. A new graphical tool — the model uncertainty curve (MUC) — is introduced to visualize the variability of model selection and to compare different model selection procedures. The MCBs methodology is implemented by a fast bootstrap algorithm that is shown to yield the correct asymptotic coverage under rather general conditions. Our Monte Carlo simulations and a real data example confirm the validity and illustrate the advantages of the proposed method.
Agent-based Asset Pricing, Learning, and Chaos
The Lucas asset pricing model is one of the most studied model in financial economics in the past decade. In our research, we relax the original assumptions in Lucas model of homogeneous agents and rational expectations. We populate an artificial economy with heterogeneous and boundedly rational agents. By defining a Correct Expectations Equilibrium, agents are able to compute their policy functions and the equilibrium pricing function without perfect information about the market. A natural adaptive learning scheme is given to agents to update their predictions. We examine the convergence of equilibrium with this learning scheme and show that the equilibrium is learnable (convergent) under certain parameter combinations. We also investigate the market dynamics when agents are out of equilibrium, including the cases where prices have excess volatility and the trading volume is high. Numerical simulations show that our system exhibits rich dynamics, including a whole cascade from period doubling bifurcations to chaos.