No-arbitrage commodity option pricing with market manipulation

Aïd, René, Callegaro, Giorgia and Campi, Luciano (2020) No-arbitrage commodity option pricing with market manipulation. Mathematics and Financial Economics, 14 (3). 577 - 603. ISSN 1862-9679

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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.

Item Type:	Article
Official URL:	https://www.springer.com/journal/11579
Additional Information:	© 2020 The Authors
Divisions:	Statistics
Subjects:	H Social Sciences > HG Finance
JEL classification:	C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games; Evolutionary Games; Repeated Games
Date Deposited:	23 Mar 2020 14:42
Last Modified:	12 Dec 2024 02:05
URI:	http://eprints.lse.ac.uk/id/eprint/103815

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