Pricing the (European) option to switch between two energy sources: An application to crude oil and natural gas

We consider a firm, which can choose between crude oil and natural gas to run its business. The firm selects the energy source, which minimizes its energy or production costs at a given time horizon. Assuming the energy strategy to be established over a fixed time window, the energy choice decision will be made at a given future date T. In this light, the firm's energy cost can be considered as a long position in a risk-free bond by an amount of the terminal oil price, and a short position in a European put option to switch from oil to gas by an amount of the terminal oil price too. As a result, the option to switch from crude oil to natural gas allows for establishing a hedging strategy with respect to energy costs. Modeling stochastically the underlying asset of the European put, we propose a valuation formula of the option to switch and calibrate the pricing formula to empirical data on a daily basis. Hence, our innovative framework handles widely the hedge against the price increase of any given energy source versus the price of another competing energy source (i.e. minimizing energy costs). Moreover, we provide a price for the cost-reducing effect of the capability to switch from one energy source to another one (i.e. hedging energy price risk).