On the Market Consistent Valuation of Fish Farms : Using the Real Option Approach and Salmon Futures

We consider the optimal harvesting problem for a fish farmer in a model which accounts for stochastic prices featuring a Schwartz 97 two factor price dynamics. Unlike any other literature in this context, we take account of the existence of a newly established market in salmon futures, which determines risk premia and other relevant variables, that influence the fish farmer in his decision. We consider the cases of single and infinite rotations. The value function of the harvesting problem determined in our arbitrage free setup constitutes the fair value of lease and ownership of the fish farm when correctly accounting for price risk. The data set used for this analysis contains a large set of futures contracts with different maturities traded at the Fish Pool market between 12/06/2006 and 22/03/2012