Valuation of Chemical Processes Subject to Stochastic Price Uncertainty

The valuation of commodity chemical processes is a complex function of the potential to generate economic return in a complex stochastic environment. Unlike the financial options traded in the commodity markets, chemical processes provide the owner with considerable flexibility to adjust feedstocks subject to standard stoichiometric and thermodynamic balances. We have previously reported results on a new class of thermodynamically valid steady-state models for energy utilities and solutions to the resulting valuation and hedging problems. Here we extend our approach to two new classes of processes that include steady-state stoichiometric models and commodity storage.

Abstract Our approach is to use stochastic price models for chemical commodities coupled with standard stoichometric and energy balances. Process flexibilty is modeled as degrees of freedom in a linearly constrained mass and energy balances and, additionally, the operation of a commodity storage facility. Stochastic price models include multivariate Ito-type models such as mean-reverting Ornstein-Uhlenbeck model. To maximize expected value, we employ standard results to construct the Hamilton-Jacobi-Bellman equation to assign valuation and to resolve and process degrees of freedom. 
Abstract In this paper we will outline the following results --

• Contrary to the case of simple financial options on commodities, the valuation of flexible chemical processes cannot be projected onto an underlying 'replicating portfolio' of market prices. Thus the standard assumptions of market completeness do not apply to flexible chemical processes. We therefore use arbitrage arguments to construct and upper (seller's value) and lower bounds (buyer's value) for a flexible chemical process. To the best of knowledge, this is the first report discussing the problem of incomplete markets for chemical process valuation.
• The valuation of commodity storage results in feedback control policy for optimal economic operation. We outline a generic economic model for commodity storage and demonstrate key analytical results.