Arbitrage-free valuation of exhaustible resource firms

We provide an arbitrage-free valuation of exhaustible resource firms through extending the Gibson and Schwartz (1990) model and also the Jamshidian and Fein (1990) solution to valuing an entire petroleum firm based on quoted oil futures. Our solutions are compared to accounting, traditional finance and to stockmarket valuations on a daily basis. An alternative expression of the valuations relative to stockmarket prices is in terms of the time varying implied ‘market price’ of convenience yield risk. Initial illustrations show that the implied convenience yield risk is not necessarily consistent between stockmarket and derivative market participants. Finally, we calculate the sensitivities of petroleum firm values to changes in oil prices, the convenience yield observable on NYMEX, and oil price volatilities. These partial derivatives show some of the complexities in the dynamic hedging process of using the contingent claims approach to valuing (and hedging) real assets.