Improved Value-at-Risk (VaR) Forward Curve Projection Using the Full Option Premium Profile

The predictive ability of two alternative forward price distribution forecasting methods based upon the full range of option premiums was developed and tested using 10 years of price and premium history for five traded commodities. The two models were a best-fit parametric distribution and a non-parametric linear interpolation fit. These were compared to two traditional approaches: historical time series and Black-76 option implied volatility. The forecast horizons ranged from 6 months to 1 week in duration. A modification of the theoretical results of King and Fackler (1985) nonparametric option pricing model was presented to justify the fitting of a price probability density function to the option premiums with the intrinsic value removed. Time series fits to the historical futures price indicted that the integrated ARCH (1) and GARCH (1,1) models were the most prevalent best fit to the data. For parametric fits to the option premiums, the Burr Type XII and Dagum distributions were the most prevalent best fits. Predictive ability was measured using 10-percent value-at-risk portfolio models for simple short and long futures positions where the number of actual exceptions was compared to the theoretical values. The predictive results indicated that the parametric and non-parametric distribution fits performed best on the short futures portfolios over the longer-term forecast horizons (6- and 3-months) while the Black-76 performed best over the same time horizon. For the shorter time horizons (1-month or less), the Black-76 and time series methods performed best. These results point to the possibility that a hybrid Black-76 and premium distribution fit approach (via a splice) might perform best for longer-term projections.