Modeling, Calibration and Simulation of Spot Price Paths

We introduce some popular models in the energy markets. Then we propose to incorporate a stochastic volatility feature to an existing multi-factor deterministic volatility model in order to take into account the observed implied volatility skews for each of the commodities in the simulation of monthly forward prices. As examples we consider natural gas, crude oil and heating oil price and option data. Our objective is to explore the role of stochastic volatility modeling for calibration and simulation of price paths and scenario analysis. The linkage between price, option data and modeling is captured by the so called "Vs" in our approach. These are the effective group market parameters that capture the main impact of an uncertain and fluctuating volatility, in particular how these affect prices. To explore the significance of incorporating this link we carry out an initial calibration test to explore the role of the "Vs" in the commodity price distribution. We find that indeed the distribution of the commodity prices are significantly affected by incorporating the leading correction that accounts for the effect of uncertain volatility parameters which manifests itself in the data via strong "skew" effect in the option pricing data. An added benefit of this modeling framework is that it enables us to use observations around and not only at the money in a consistent way, thus, providing robustness and stability in calibration also at the order one level.