Empirical evidence from equity markets clearly shows that the volatility of asset returns varies randomly in time. Typically, this randomness is referred to as stochastic volatility. In this article, we review how stochastic volatility can be modeled, and the use of asymptotic analysis to quantify (i) how the presence of stochastic volatility affects option prices, and (ii) how stochastic volat...

Title of dissertation: Discrete Time Stochastic Volatility Model Guojing Tang, Doctor of Philosophy, 2009 Dissertation directed by: Professor Dilip B. Madan Professor Benjamin Kedem In this dissertation we propose a new model which captures observed features of asset prices. The model reproduces the skewness and fat tails of asset returns by introducing a discretized variance gamma process as t...

This paper introduces a new class of stochastic volatility models which allows for stochastic volatility of volatility. Such models are given by volatility modulated non–Gaussian Ornstein Uhlenbeck processes. We study the probabilistic properties of such models both under the physical and under the risk neutral probability measure, where we focus in particular on the role of the volatility of v...

An estimation method is developed for extracting the latent stochastic volatility from VIX, a volatility index for the S&P 500 index return produced by the Chicago Board Options Exchange (CBOE) using the so-called model-free volatility construction. Our model specification encompasses all mean-reverting stochastic volatility option pricing models with a constant-elasticity of variance and those...

In this chapter we use particle filtering methods to estimate volatility and examine volatility dynamics for three financial time series during the early part of the current credit crisis. We compare estimates from a pure stochastic volatility model, a stochastic volatility model with jumps and a Garch model to each other and to the market volatilities implied by actual option prices. Our three...

Abstract We study the effect of an asset’s volatility on expected returns European options asset. Deriving predictions from a stochastic discount factor model, we show that depends whether variations in are driven by systematic or idiosyncratic volatility. While idiosyncratic-volatility-induced only affect option elasticity, systematic-volatility-induced also oppositely return Since asset (elas...