Optimal Rotation Time in Fish Farming. An Option Approach
By Atle Guttormsen
ABSTRACT
A standard assumption on optimal slaughtering in fish farming is that fish prices are constant over time. Prices do, however, fluctuate. This paper models prices as a lognormal diffusion process. A natural way of handling uncertainty in slaughtering decisions is to apply a "real options" approach. The owner of a fishpond (or pen) holds a call option, i.e. an option to "buy" fish at an exercise price (strike), i.e. the cost of slaughtering. The option is "American" since the owner may exercise the option at any time between then and the day the fish becomes so old that the probability for death or sexual maturity approaches unity. Once the option is exercised (i.e., the fish is slaughtered), the owner receives money for the fish and also a new option, i.e. vacant space in the pen. Calculating the value of such an option does not require predictions of prices far into the future. The only assumption about prices in the future is that they follow certain well-defined st!ochastic processes. To value the option and find the optimal exercise (slaughtering) time, we use a two-state option-pricing model, known as the "binomial option pricing model". Numerical solutions for several species are computed using the familiar technique of dynamic programming. Comparing the diffusion results modeled here to the fixed price results shows that the prescribed rotation length in general is longer in the former case.
KEYWORDS: Fish Farming, Harvesting, Real Options, Tilapia
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