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Theory of Storage and Option Pricing: Analyzing Determinants of Implied Skewness and Implied Kurtosis

Options on agricultural futures are popular financial instruments used for agricultural price risk management and to speculate on future price movements. Poor performance of Black’s classical option pricing model has stimulated many researchers to introduce pricing models that are more consistent with observed option premiums. However, most models are motivated solely from the standpoint of the time series properties of futures prices and need for improvements in forecasting and hedging performance. In this paper we propose a novel arbitrage pricing model motivated from the economic theory of optimal storage. We introduce a pricing model for options on futures based on a Generalized Lambda Distribution (GLD) that allows greater flexibility in higher moments of the expected terminal distribution of futures price. We show how to use high-frequency data to estimate implied skewness and kurtosis parameters. We propose an economic explanation for variations in skewness based on the theory of storage. We use times and sales data for corn futures and options on futures for the period 1995-2009. After controlling for changes in planned acreage, we find a statistically significant negative relationships between ending stocks-to-use and implied skewness and kurtosis, as predicted by the theory of storage.

arbitrage pricing model; options on futures; generalized lambda distribution; theory of storage; skewness; kurtosis

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