No-Arbitrage Commodity Option Pricing with Market Manipulation

TL;DR

This paper develops three continuous-time models of commodity prices affected by market manipulation, providing semi-explicit solutions and analyzing the strategic interactions between producers and traders in derivative pricing.

Contribution

It introduces novel models capturing market manipulation effects on commodity prices and derives closed-form solutions for derivative pricing under these conditions.

Findings

Producer can offset profit loss by manipulating volatility.

Active traders influence market dynamics, creating a game-theoretic scenario.

Existence of mutually beneficial strategies for producers and traders.

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.