Abstract
We design three continuous-time models in finite horizon of a commodity price, whose dynamics can be affected by the actions of a representative risk-neutral producer and a representative risk-neutral trader. Depending on the model, the producer can control the drift and/or the volatility of the price whereas the trader can at most affect the volatility. The producer can affect the volatility in two ways: either by randomizing her production rate or, as the trader, using other means such as spreading false information. Moreover, the producer contracts at time zero a fixed position in a European convex derivative with the trader. The trader can be price-taker, as in the first two models, or she can also affect the volatility of the commodity price, as in the third model. We solve all three models semi-explicitly and give closed-form expressions of the derivative price over a small time horizon, preventing arbitrage opportunities to arise. We find that when the trader is price-taker, the producer can always compensate the loss in expected production profit generated by an increase of volatility by a gain in the derivative position by driving the price at maturity to a suitable level. Finally, in case the trader is active, the model takes the form of a nonzero-sum linear-quadratic stochastic differential game and we find that when the production rate is already at its optimal stationary level, there is an amount of derivative position that makes both players better off when entering the game.
Highlights
The methods and techniques of manipulation are limited only by the ingenuity of man, in Cargill vs Hardin, US Court of Appeal, 8th circuit, December 7, 1971.Price manipulation in financial markets is not the rare event as one may think
In their report for the Federal Reserve Bank of New York on the LIBOR scandal, Hou and Skeie [14] explain that if the first motivation for this manipulation in the aftermath of the 2008 financial crisis was to maintain a signal of credit worthiness, the second motivation was the express intent of benefiting the bank’s derivatives positions
Manipulation of the commodity price comes at some costs, which are included in their profit functions
Summary
The methods and techniques of manipulation are limited only by the ingenuity of man, in Cargill vs Hardin, US Court of Appeal, 8th circuit, December 7, 1971. We take market price manipulation models one step further in considering the possibility of the joint control of the average (the drift) and of the volatility of a commodity price by the actions of a producer and a trader who exchange a derivative. Regarding the use of information on the volatility, we suppose that the trader or the producer has identified some channels allowing her to act on the nominal volatility of the underlying by an appropriate rate of information For both agents, manipulation of the commodity price comes at some costs, which are included in their profit functions.
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