State-of-the-art stochastic volatility models generate a “volatility smirk” that explains why out-
of-the-money index puts have high prices relative to the Black-Scholes benchmark. These …

Realized volatility is a nonparametric ex-post estimate of the return variation. The most
obvious realized volatility measure is the sum of finely-sampled squared return realizations …

Volatility indices are becoming increasingly popular as a measure of market uncertainty and
as a new asset class for developing derivative instruments. Although jumps are widely …

We compare density forecasts of the S&P 500 index from 1991 to 2004, obtained from option
prices and daily and 5-min index returns. Risk-neutral densities are given by using option …

We give an overview of a broad class of models designed to capture stochastic volatility in
financial markets, with illustrations of the scope of application of these models to practical …

Option prices provide a great deal of information regarding the market's expectations of
future asset price dynamics. But, the implied dynamics are under the risk-neutral measure …

This paper analyzes exponentially affine and non-affine stochastic volatility models with
jumps in returns and volatility. Markov Chain Monte Carlo (MCMC) technique is applied …

This paper examines continuous-time models for the price and volatility processes of
individual stocks and the S\&P 100 index via Markov Chain Monte Carlo estimation. We find …

This chapter surveys filtering methods, where the state of an unobserved dynamic model is
inferred based on noisy observations. In linear and gaussian models, the Kalman Filter is …

This chapter reviews some of the key issues involved in estimating continuous-time
stochastic volatility models. Such models have become popular recently because they …