A multi-period equilibrium pricing model of weather derivatives

Abstract

The prevalence of commercial activities whose profit and cost are correlated with weather risk makes weather derivatives valuable financial instruments that enable hedging of price or volumetric (quantity) risk in many industries. This paper proposes a multi-period equilibrium pricing model for weather derivative. In our stylized economy representative agents of weather-sensitive industries optimizes their hedging portfolios that drive the supply and demand for weather derivative which are dynamically determined based on a utility indifference pricing framework. At equilibrium the weather derivative market will be cleared and their market price can be obtained. Numerical examples illustrate the equilibrium prices and optimal choices for the weather derivative as function of the correlation between weather indices and demand for the underlying commodity. We also demonstrate the benefit of multiple trading opportunities which allows rebalancing of the hedging portfolio prior to the commodity delivery date, as compared to a single shot framework.

A Multiperiod Equilibrium Pricing Model

“…Cao and Wei [6], Lee and Oren [7,8], and Cheridito et al [9] are related to our work. Cao and Wei [6] generalize the model of Lucas [10] to provide an equilibrium framework for valuing weather derivatives in a multiperiod setting.…”

“…Lee and Oren [7] explore a single-period equilibrium pricing model in a multicommodity setting and mean-variance preferences. Lee and Oren [8] made a followup in a multiperiod framework. Cheridito et al [9] establish results on the existence and uniqueness of equilibrium in dynamically incomplete financial markets with preferences of monetary type and heterogeneous agents.…”

A Multi Period Equilibrium Pricing Model

“…Cao and Wei [6], Lee and Oren [7,8], and Cheridito et al [9] are related to our work. Cao and Wei [6] generalize the model of Lucas [10] to provide an equilibrium framework for valuing weather derivatives in a multiperiod setting.…”

A Dynamic Programming Approach for Pricing Weather Derivatives under Issuer Default Risk

“…Most previous works on utility-based WD pricing either fail to price derivatives on multiple dependent underlying indices simultaneously (Carmona and Diko 2005;Lee and Oren 2010;Leobacher and Ngare 2011) or they impose restrictive assumptions on the dynamics of the underlying weather indices (Horst and Müller 2007;Chaumont et al 2006). Consumption based model of Cao and Wei (2004) prices multiple WDs in an extended pure exchange economy of Lucas (1978) on the macroeconomic level and is not feasible for a limited number of weather market participants and a short contract duration typical for OTC markets.…”