Essays on natural resource evaluation and management
Derivatives markets, in particular futures markets, play an important role in the organization of production in commodity markets. While commodity markets for agricultural and natural resources like live cattle, soybean, oil, gas and minerals are well established, commodity markets for marine resources are very new. Located in Bergen (Norway), Fish Pool is a new derivatives market, where futures contracts written on fresh farmed salmon are traded in large quantities since 2006, continuing a strong upwards trend. Markets for forwards and futures on fresh salmon help companies which use fresh salmon in their production, for example, food processing companies, to hedge their price risk and plan ahead, by fixing the price in advance. In the same way, they help producers, i.e. salmon farmers, to reduce their selling price risk. In fact, according to Fish Pool News Archive released on 20/03/2012, not only consumers, processors and producers, but also speculative investors at Fish Pool play a more and more important role, which in consequence urges the issue of finding appropriate, theoretical well-founded and sound pricing formulas for the futures contracts traded there, as well as examining its effects on participants. 

In this PhD thesis, we first discuss the valuation of futures on fresh farmed salmon as traded on the Fish Pool exchange and then explore how information reflected in the prices of futures contracts can be used to compute fair prices, i.e., arbitrage free prices, for lease and ownership of fish farms. Specifically, in the first chapter, we give a general background of the study and introduce the estimation methods adopted in the thesis, i.e., Kalman filter combined with the maximum likelihood estimation. In Chapter 2, we connect the popular Schwartz (1997) multi-factor approach, which features a stochastic convenience yield for the salmon spot price, with the classical literature on fish farming and aquaculture. We follow first principles, starting by modeling the aggregate salmon farming production process and modeling the demand using a Cobb-Douglas utility function for a representative consumer. In Chapter 3, we extend the Schwartz (1997) two-factor model by adding a seasonality feature to the mean-level of convenience yield. All models are estimated by means of Kalman filter, using a rich data set of contracts with different maturities traded at Fish Pool. The estimates are also discussed in the context of other commodity markets, specifically live cattle which acts as a substitute. Our results show that the framework presented is able to produce an excellent fit to the actual term structure of salmon futures. A comparison with live cattle futures traded within the same period reveals subtle differences, for example within the level of the convenience yield, the speed of mean reversion of the convenience yield and the convenience yield risk premium. In Chapter 4, we consider the optimal harvesting problem for a fish farmer. We take account of the existence of Fish Pool, which determines risk premia and other relevant variables, that influence the fish farmer in his decision. We assess the optimal strategy, harvesting time and value against two alternative setups. The first alternative involves simple strategies which 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. In consequence, for a risk-averse fish farmer, the presence of a salmon futures market, as well as managerial flexibility, are highly important.