The market for salmon futures: an empirical analysis of the Fish Pool using the Schwartz multi-factor model

Abstract

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 modelling the aggregate salmon farming production process and modelling 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 June 2006 and 22 June 2012. The results are then discussed in the context of other commodity markets, specifically for live cattle which acts as a substitute.

Keywords:

• Futures
• Commodities
• Aquaculture
• Fisheries Economics
• Agricultural economics
• Risk management

Notes

No potential conflict of interest was reported by the authors.

1 Compare Fish Pool News Archive, 20 March 2012.

2 More precisely, denotes the augmented and completed filtration generated by the Brownian motions , and .

3 The oligopolistic aquaculture harvesting problem does not seem to have been discussed in the literature.

4 Note that while individual farmers still do complete harvests rather than continuously harvesting a proportion of the biomass, in aggregation the affect is like continuous harvesting. Even for a single salmon farming unit consisting of multiple pens, it would be unwise to harvest all pens at once.

5 The Fish Pool price index is based on a weighted weekly average of salmon categories 3–4 kg: 30%, 4–5 kg: 40%, 5–6 kg: 30%, superior quality, head-on gutted. Further details are available on http://fishpool.asp.manamind.com/?page_id=65.

6 As at this point can be an arbitrary stochastic process, the only assumption made here is that the volatility of is proportional to its level, which is a simplifying but intuitive assumption.

7 Average interest rate r over the whole sample time period is 2.13%.

8 In the context of the two-factor model, where there is only one relevant correlation, we omit sub-indices and denote .

9 The figures for Panel B and C look similar, but are omitted due to space limitations.

10 The slightly odd looking actual term structure for longer dated salmon future contracts is likely to be caused by the rather low trading volume of these contracts.

11 Note that for the ’s for both cattle and salmon are insignificant.