Analysis of the risk premium in the forward market for salmon
Introduction
In this paper we analyse the risk premium in the forward market for salmon using stochastic modelling and pricing techniques from financial mathematics. At the Fish Pool2 market one can trade in forward contracts with delivery of salmon. The contracts are financially settled against the weekly announced Fish Pool Index (FPI), over a monthly settlement period. This means that a long position in a forward contract will give the value of the FPI over the settlement period in return for the agreed forward price.
Typically in commodity markets, a forward contract is settled with delivery of the commodity at a given time, the so-called delivery time. The forward price is derived by predicting the spot price of the commodity at delivery, based on a risk adjustment, and will become an explicit function of the current spot price. This risk adjustment includes storage costs, liquidity premium, convenience yield and other market frictions. We refer to Geman (2005) for a discussion of various commodity forward markets. The only financial instrument that exists in the world on marine resources involves futures contracts on the Norwegian Fish Pool Index (FPI, http://fishpool.eu/), which reflects the spot price for fish products, mainly fresh, farmed Atlantic salmon (Salmo salar). In the case of the Fish Pool forwards, the “spot” is the FPI, with the peculiar feature that forwards can be traded in the market daily, whereas the “spot” is an index only announced every Tuesday. Hence, in their trading operation, actors in fish contracts must base their forward prices on predictions of the FPI except on Tuesdays when it is revealed.
The Fish Pool Index (FPI) has been derived to provide a reference price reflecting the actual spot price of fresh Atlantic Salmon and is the basis for settlement of all financial salmon contracts at Fish Pool. It is based on three indices; the Nasdaq Salmon Index (Exporter's selling prices), Fish Pool European Buyers Index (Large purchasers purchase price) and Statistics Norway customs statistics (SSB; Norwegian export statistics, ssb.no), and calculated as a monthly settlement price based on the 4–5 weekly price elements. All financial contracts at Fish Pool are settled on a monthly basis against FPI, which is published weekly on fishpool.eu.
To follow the framework for no-arbitrage pricing of forward contracts in commodity markets like energy, weather, precious metals etc. (see Geman (2005), Benth et al. (2008a), (Benth and Šaltytė Benth, 2013)), we will in this paper develop a forward price dynamics based on a continuous-time stochastic process. Thus, we will assume that the market observes the FPI continuously over time. This is a bold approximation over reality, but as we will see, our approach will provide us with a term structure dynamics reflecting the qualitative behaviour of the observed market prices rather closely. In Fig. 1 we show four different forward curves observed over the years in the Fish Pool market. Each of the curves consist of 60 forward prices at a given date, and we clearly see that in the long end of the market, prices are constant as a function of the settlement time. On the other hand, in the shorter end of the market, the term structure of the forward prices depict a much more complex behaviour with bumps in the very short end and also farther out on the curve. Over time, the forward curves change in shape and also show a variation in the long end prices. Motivated by these shapes, we propose a two-factor stochastic dynamics for the FPI, based on a non-stationary part and a continuous-time autoregressive moving average dynamics for the stationary part. Although the market only observes the FPI on Tuesdays, we propose a model being continuous over time accounting for the possibility that traders can make qualified assessments on the “current FPI”. Using this model, we derive analytical forward prices from conditional risk-adjusted expected values of the FPI over the settlement period. We remark that our model for the FPI, although being classified as a two-factor model analogous to Schwartz and Smith (2000) (see also Gibson and Schwartz (1990) and Lucia and Schwartz (2002)), is novel in the sense that we find a non-stationary compound Poisson process as the long-term factor, combined with a higher-order autoregressive short term factor.
From an empirical analysis based on a history of observed FPI data along with a long record of historical Fish Pool forward prices, we calibrate our model. The non-stationary FPI factor will describe the long end variations of the forward curve, while the continuous-time autoregressive dynamics will be sufficiently flexible in order to account for the complex shapes like those we see in Fig. 1. We apply our stochastic model to analyse the risk premium in the Fish Pool market, defined as the difference between the forward prices and the predicted FPI over the corresponding settlement periods. We find that the risk premium in the long end of the market is negative, consistent with the normal backwardation theory of producers putting on a hedging pressure. However, in the shorter end of the market we find a risk premium with a randomly changing sign, indicating that also the demand-side of the fish market puts on a significant hedging pressure. This interesting feature of the fish market is shared with other “exotic” forward markets like power (see Benth et al. (2008b). Geman and Vasicek (2001) argues that the retailers in power market use forwards as a protection against sudden high prices. Indeed, their argument holds for non-storable commodities. Our results indicate a similar situation for the Fish Pool forward market.
Asche, Misund and Oglend (2016) analyse empirically the risk premium in the salmon market, based on a similar data set to ours. More specifically, they analyse and quantify the impact that the futures-spot basis, seasonality and various industry-specific variables like seawater temperatures and biomass, has on the risk premium. Their study is based on the approach of French and Fama, 1987, French and Fama, 1988, where the risk premium can be investigated empirically through regression. Among other results, the risk premium calculated for the front month contracts is stochastically fluctuating with a changing sign. Our study differs from Asche et al. (2016) in that we propose a stochastic dynamics for both the FPI spot and forward prices, and apply these as the starting point for an analysis of the risk premium. Our findings are in line with the empirical risk premium found in the short end of the market by Asche et al. (2016). The FPI data have also been investigated before in related models (Ewald (2013), Ewald and Salehi (2015)); however, they have used different models with different focus than ours.
Our results are presented as follows: In Section 2 we present the stochastic model for the FPI along with a derivation of theoretical forward prices. Some analysis of the model is also performed, useful for the empirical analysis of FPI and Fish Pool forward contracts presented in Section 3. The next section contains an empirical study of the risk premium, before we conclude in the last section.
Section snippets
A continuous-time forward price model
In this section we define a spot dynamics for the FPI generalizing the two-factor model of Schwartz and Smith (2000) (see also Gibson and Schwartz (Schwartz and Smith, 2000) and Lucia and Schwartz (2002)), where the stationary part is modelled using a higher-order continuous-time autoregressive process. From the FPI dynamics we derive forward prices for the salmon market.
Let define a complete probability space, equipped with a filtration . Recall from Brockwell (2001) that a
Data description and empirical analysis
In this Section we estimate our proposed stochastic model for the spot and foward prices on salmon to observed data. The empirical analysis is performed on a data set of FPI index quotes and forward prices obtained from the Fish Pool.3
The Fish Pool organizes trade in salmon forward contracts
Empirical study of the risk premium
The risk premium is defined to be the difference between the actual forward price and predicted spot for a given settlement period. If the settlement period is [T1, T2], the predicted price is defined as
Our theoretical forward price is recovered using the expectation with respect to Q rather than P inside the integral above. We find from Prop. 7 thatwithfor x ≥ 0. Notice that we have
Conclusion
All species adapt to their surrounding environments, and farmed salmon living in the ocean may be affected by climate change. Furthermore, climate change may have a severe impact on the world economy (Dietz et al. (2016)). Our results highlight an opportunity for future research on the underlying assumptions in financial models to understand if and how changes in climate and biodiversity may affect the financial markets (Reeves et al. (2012), Dalton (2005), Galaz et al. (2015)). In this paper
Acknowledgement
A.M.E. and S.A.L. acknowledge the project “Green Growth Based on Marine Resources: Ecological and Socio-Economic Constraints (GreenMAR) for funding by Nordforsk.
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2022, Knowledge-Based SystemsCitation Excerpt :Asche et al. [8] studied the spot-forward relationship by treating futures price with maturities up to six months as an unbiased estimator of spot prices. The popular two-factor commodity model for spot prices, with a stochastic convenience yield explicitly included, is widely applied to examine salmon futures prices and aquaculture-farming considerations (Benth et al. [9]). Alternatively, research investigations would also focus directly on futures prices when performing the analysis of the Fish Pool salmon market.
Determinants of investment behavior in Norwegian salmon aquaculture
2023, Aquaculture Economics and Management
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The authors are listed in alphabetical order.