An analysis of the fish pool market in the context of seasonality and stochastic convenience yield

On the basis of a popular two-factor approach applied in commodity markets, we develop a model featuring seasonality and study futures contracts written on fresh farmed salmon, which have been actively traded at the Fish Pool market in Norway since 2006. The model is estimated by means of Kalman filtering, using a rich data set of contracts with different maturities traded at Fish Pool between 01/01/2010 and 24/04/2014. The results are then discussed in the context of other commodity markets, specifically live cattle, which is a substitute. We show that the seasonally adjusted model proposed in this article describes the behavior of salmon price very well. More importantly we show that seasonality exists in the salmon futures market. This is highly important in pricing of contingent claims, designing hedging strategies, and making real investment decisions in marine resources

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 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 12/06/2006 and 22/03/2012. 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

The market for salmon futures: an empirical analysis of fish pool using the Schwartz multifactor model

Using the popular Schwartz 97 two-factor approach, we study future contracts written on fresh farmed salmon, which have been actively traded at the Fish Pool Market in Norway since 2006. This approach features a stochastic convenience yield for the salmon spot price. We connect this approach with the classical literature on fish-farming and aquaculture using 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. The model is estimated by means of Kalman filtering, using a rich data set of contracts with different maturities traded at Fish Pool between 12/06/2006 and 22/03/2012. The results are then discussed in the context of other commodity markets, specifically live cattle which acts as a substitute

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

Pricing commodity futures and determining risk premia in a three factor model with stochastic volatility: the case of Brent crude oil

In this paper we introduce a three factor model to price commodity futures contracts. This model allows both the spot price volatility and convenience yield to be stochastic, nevertheless futures prices can be obtained conveniently in closed form. Further, we use Brent crude oil futures prices to calibrate the model using the extended Kalman filter. In comparison to the benchmark model for commodity futures pricing, the Schwartz two-factor model, our three factor model shows a superior fit for contracts that have longer maturities. We further assess risk premia in Brent crude oil through the two models and observe that the Schwartz two-factor model over-predicts risk premia in comparison to the new model