Viktor Todorov

Tails, Fears and Risk Premia

We show that the compensation for rare events accounts for a large fraction of the average equity and variance risk premia. Exploiting the special structure of the jump tails and the pricing thereof we identify and estimate a new Investor Fears index. The index suggests both large and time-varying compensations for fears of disasters. Our empirical investigations are essentially model-free, involving new extreme value theory approximations and high-frequency intraday data for estimating the expected jump tails under the statistical probability measure, and short maturity out-of-the money options and new model-free implied variation measures for estimating the corresponding risk neutral expectations.

Jumps and Betas: A New Framework for Disentangling and Estimating Systematic Risks

We provide a new theoretical framework for disentangling and estimating sensitivity towards systematic diffusive and jump risks in the context of factor pricing models. Our estimates of the sensitivities towards systematic risks, or betas, are based on the notion of increasingly finer sampled returns over fixed time intervals. In addition to establishing consistency of our estimators, we also derive Central Limit Theorems characterizing their asymptotic distributions. In an empirical application of the new procedures using high-frequency data for forty individual stocks and an aggregate market portfolio, we find the estimated diffusive and jump betas with respect to the market to be quite different for many of the stocks. Our findings have direct and important implications for empirical asset pricing finance and practical portfolio and risk management decisions.

Do price and volatility jump together

We consider a process

Simulation Methods for Levy-Driven Continuous-Time Autoregressive Moving Average (CARMA) Stochastic Volatility Models

X_t

The Realized Laplace Transform of Volatility

, which is observed on a finite time interval

Simulation Methods for Levy-Driven CARMA Stochastic Volatility Models

[0,T]

Limit theorems for power variations of pure-jump processes with application to activity estimation

, at discrete times

Realized Laplace transforms for pure-jump semimartingales

0,\Delta_n,2\Delta_n,\ldots.

Volatility occupation times

This process is an It\^{o} semimartingale with stochastic volatility

Inverse Realized Laplace Transforms for Nonparametric Volatility Density Estimation in Jump-Diffusions

\sigma_t^2