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 that accounts for stochastic prices featuring Schwartz (1997) 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 risk-averse fish farmers in their harvesting 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 values 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 June 12, 2006 and March 22, 2012. We assess the optimal strategy, harvesting time, and value against two alternative setups. The first alternative involves simple strategies that lack managerial flexibility; the second alternative allows for managerial flexibility and risk aversion as modeled by a constant relative risk aversion utility function, but without access to the salmon futures market. In both cases, the loss in project value can be very significant, and in the second case is only negligible for extremely low levels of risk aversion. As a consequence, for a risk-averse fish farmer, the presence of a salmon futures market as well as managerial flexibility are highly important.