Financial engineering in pricing agricultural derivatives based on demand and volatility

Abstract

Purpose – The purpose of this paper is twofold. First, the author proposes a financial engineering framework to model commodity prices based on market demand processes and demand functions. This framework explains the relation between demand, volatility and the leverage effect of commodities. It is also shown how the proposed framework can be used to price derivatives on commodity prices. Second, the author estimates the model parameters for agricultural commodities and discuss the implications of the results on derivative prices. In particular, the author see how leverage effect (or inverse leverage effect) is related to market demand. Design/methodology/approach – This paper uses a power demand function along with the Cox, Ingersoll and Ross mean-reverting process to find the price process of commodities. Then by using the Ito theorem the constant elastic volatility (CEV) model is derived for the market prices. The partial differential equation that the dynamics of derivative prices satisfy is found and, by the Feynman-Kac theorem, the market derivative prices are provided within a Monte-Carlo simulation framework. Finally, by using a maximum likelihood estimator, the parameters of the CEV model for the agricultural commodity prices are found. Findings – The results of this paper show that derivative prices on commodities are heavily affected by the elasticity of volatility and, consequently, by market demand elasticity. The empirical results show that different groups of agricultural commodities have different values of demand and volatility elasticity. Practical implications – The results of this paper can be used by practitioners to price derivatives on commodity prices and by insurance companies to better price insurance contracts. As in many countries agricultural insurances are subsidised by the government, the results of this paper are useful for setting more efficient policies. Originality/value – Approaches that use the methodology of financial engineering to model agricultural prices and compute the derivative prices are rather new within the literature and still need to be developed for further applications.