Pricing Commodity Options when the Underlying Futures Price Exhibits Time‐Varying Volatility

Abstract

This paper outlines a model for pricing options when the underlying futures pnce exhibits time-varying volatility. Futures price movements are characterized using a GARCH model. In an empirical application, the GARCH option pricing model predicts market premmms significantly better than the standard Black model, which assumes volatility is constant.

Testing Option Pricing Models

“…Studies that have tested ARCH-based volatility assessments on option prices include Cao (1992) for currency options, Myers and Hanson (1993) for commodity options, and Amin and Ng (1993) for stock options. All three papers use ARCH-based volatility assessments as inputs to both an ad hoc Black-Scholes option pricing model and the ARCH option pricing model.…”

“…The reasons for the superior performance are unclear. Myers and Hanson (1993) estimated a rolling-regression GARCH(1,1)/Student's t process for soybean futures. They found that the major gain for soybean futures option pricing prediction relative to Black's (1976b) geometric Brownian motion model originated in the GARCH recognition of volatility mean reversion.…”

On the exit value of a forward contract

“…These stylized facts have also been documented for other commodities (Baillie & Myers, 1991;Myers & Hanson, 1993;Roberts, 2000;Yang & Brorsen, 1992).…”

The planting real option in cash rent valuation

“…The distributional properties of the three data series generally appear non-normal as indicated by sample skewness and kurtosis values. In addition, compared with the multivariate normal distribution assumption of The price simulation method used in this study is an extension to the multivariate setting of Myers and Hanson (1993). One-step-ahead forecasts of variance-covariance matrices are recursively generated by the BEKK model, given as (21)Ĥ t+1 =Ĉ Ĉ + ε t ε t +B H tB whereĈ,Â, andB are estimated model parameters, ε t is the error from the last observation in the sample used to estimate the MGARCH model, and H t is the time t sample variancecovariance matrix.…”