In this companion paper to “Optimal Investment with Transaction Costs and Stochastic Volatility Part I: Infinite Horizon”, we give an accuracy proof for the finite time optimal investment and consumption problem under fast mean-reverting stochastic volatility of a joint asymptotic expansion in a time scale parameter and the small transaction cost. AMS subject classification 91G80, 60H30. JEL su...

We consider the problem of pricing European forward starting options in the presence of stochastic volatility. By performing a change of measure using the asset price at the time of strike determination as a numeraire, we derive a closed-form solution based on Heston’s model of stochastic volatility.

This paper considers the pricing of options when there are jumps in the pricing kernel and correlated jumps in asset prices and volatilities. We extend theory developed by Nelson (1990) and Duan (1997) by considering limiting models for our resulting approximating GARCH-Jump process. Limiting cases of our processes consist of models where both asset price and local volatility follow jump diffus...

We provide a detailed summary of the large and vibrant emerging literature that deals with the multivariate modeling of conditional volatility of financial time series within the framework of stochastic volatility. The developments and achievements in this area represent one of the great success stories of financial econometrics. Three broad classes of multivariate stochastic volatility models ...

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...