Commodity derivatives are becoming an increasingly important part of the global derivatives market. Here we develop a tractable stochastic volatility model for pricing commodity derivatives. The model features unspanned stochastic volatility, quasi-analytical prices of options on futures contracts, and dynamics of the futures curve in terms of a low-dimensional affine state vector. We estimate ...

We present a family of hedging strategies for a European derivative security in a stochastic volatility environment. The strategies are robust to speciication of the volatility process and do not need a parametric description of it or estimation of the volatility risk premium. They allow the hedger to control the probability of hedging success according to risk aversion. The formula exploits th...

In the electricity market, spark-spread options are increasingly used for hedging purposes and for valuing natural gas power plants. A spark-spread option gives the buyer the right but not the obligation to buy the price difference between electricity and natural gas adjusted for power plant efficiency. Pricing these options requires stochastic process models for the electricity price and the g...

This paper describes an parallel semi-Lagrangian nite diierence approach to the pricing of early exercise Asian Options on assets with a stochastic volatility. A multigrid procedure is described for the fast iterative solution of the discrete linear complementarity problems that result. The accuracy and performance of this approach is improved considerably by a strike-price related analytic tra...

The most common stochastic volatility models such as the Ornstein–Uhlenbeck (OU), the Heston, the exponential OU (ExpOU) and Hull–White models define volatility as a Markovian process. In this work we check the applicability of the Markovian approximation at separate times scales and will try to answer the question which of the stochastic volatility models indicated above is the most realistic....

Many asset classes, such as interest rates, exchange rates, commodities, and equities, often exhibit a strong relationship between asset prices and asset volatilities. This paper examines an analytical model that takes into account this level dependence of volatility. We demonstrate how prices of European options under stochastic volatility can be calculated analytically via inverse Laplace tra...

We show that, for three common SARV models, fitting a minimum mean square linear filter is equivalent to fitting a GARCH model. This suggests that GARCH models may be useful for filtering, forecasting, and parameter estimation in stochastic volatility settings. To investigate, we use simulations to evaluate how the three SARV models and their associated GARCH filters perform under controlled co...

Classical (Itô diffusions) stochastic volatility models are not able to capture the steepness of smallmaturity implied volatility smiles. Jumps, in particular exponential Lévy and affine models, which exhibit small-maturity exploding smiles, have historically been proposed to remedy this (see [53] for an overview). A recent breakthrough was made by Gatheral, Jaisson and Rosenbaum [27], who prop...

We consider a stochastic volatility model where the volatility process is a fractional Brownian motion. We estimate the memory parameter of the volatility from discrete observations of the price process. We use criteria based on Malliavin calculus in order to characterize the asymptotic normality of the estimators. 2000 AMS Classification Numbers: 60F05, 60H05, 60G18.