We are concerned with investment decisions when the spanning asset that correlates with the investment value undergoes a stochastic volatility dynamics. The project value in this case corresponds to the value of an American call with dividends, which can be priced by solving a generalized Black-Scholes free boundary value problem. Following ideas of Fouque et al., under the hypothesis of fast m...

The views expressed herein are those of the author(s) and do not necessarily reflect the views of the National Bureau of Economic Research. ABSTRACT We conduct a comprehensive analysis of unspanned stochastic volatility in commodity markets in general and the crude-oil market in particular. We present model-free results that strongly suggest the presence of unspanned stochastic volatility in th...

We study infinite–horizon, optimal switching problems under a general class of stochastic volatility models that exhibit “fast” mean–reversion by using techniques from homogenisation theory. This leads to perturbation theory, providing closed–form approximations to the full switching problem which is often intractable, both analytically and numerically. We apply our general results to certain, ...

Substantial progress has been made in developing more realistic option pricing models. Empirically, however, it is not known whether and by how much each generalization improves option pricing and hedging. We ll this gap by rst deriving an option model that allows volatility, interest rates and jumps to be stochastic. Using S&P 500 options, we examine several alternative models from three persp...

This paper examines two asymmetric stochastic volatility models used to describe the heavy tails and volatility dependencies found in most financial returns. The first is the autoregressive stochastic volatility model with Student’s t-distribution (ARSV-t), and the second is the multifactor stochastic volatility (MFSV) model. In order to estimate these models, the analysis employs the Monte Car...

Numerical integration methods for stochastic volatility models in financial markets are discussed. We concentrate on two classes of stochastic volatility models where the volatility is either directly given by a mean-reverting CEV process or as a transformed Ornstein-Uhlenbeck process. For the latter, we introduce a new model based on a simple hyperbolic transformation. Various numerical method...

We develop a rational expectations model of financial bubbles and study ways in which a generic risk-return interplay is incorporated into prices. We retain the interpretation of the leading Johansen-Ledoit-Sornette model, namely, that the price must rise prior to a crash in order to compensate a representative investor for the level of risk. This is accompanied, in our stochastic model, by an ...

The literature on volatility modelling and option pricing is a large and diverse area due to its importance and applications. This paper provides a review of the most significant volatility models and option pricing methods, beginning with constant volatility models up to stochastic volatility. We also survey less commonly known models e.g. hybrid models. We explain various volatility types (e....

We provide a formulation of stochastic volatility based on Gaussian processes, a flexible framework for Bayesian nonlinear regression. The advantage of using Gaussian processes in this context is to place volatility forecastingwithin a regression framework; this allows a large number of explanatory variables to be used for forecasting, a task difficult with standard volatility-forecasting formu...