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A McKean-Vlasov game of commodity production, consumption and trading

Author

Listed:
  • Ren'e Aid
  • Ofelia Bonesini
  • Giorgia Callegaro
  • Luciano Campi

Abstract

We propose a model where a producer and a consumer can affect the price dynamics of some commodity controlling drift and volatility of, respectively, the production rate and the consumption rate. We assume that the producer has a short position in a forward contract on \lambda units of the underlying at a fixed price F, while the consumer has the corresponding long position. Moreover, both players are risk-averse with respect to their financial position and their risk aversions are modelled through an integrated-variance penalization. We study the impact of risk aversion on the interaction between the producer and the consumer as well as on the derivative price. In mathematical terms, we are dealing with a two-player linear-quadratic McKean-Vlasov stochastic differential game. Using methods based on the martingale optimality principle and BSDEs, we find a Nash equilibrium and characterize the corresponding strategies and payoffs in semi-explicit form. Furthermore, we compute the two indifference prices (one for the producer and one for the consumer) induced by that equilibrium and we determine the quantity \lambda such that the players agree on the price. Finally, we illustrate our results with some numerics. In particular, we focus on how the risk aversions and the volatility control costs of the players affect the derivative price.

Suggested Citation

  • Ren'e Aid & Ofelia Bonesini & Giorgia Callegaro & Luciano Campi, 2021. "A McKean-Vlasov game of commodity production, consumption and trading," Papers 2111.04391, arXiv.org.
  • Handle: RePEc:arx:papers:2111.04391
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    References listed on IDEAS

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    1. A. Bensoussan & K. C. J. Sung & S. C. P. Yam & S. P. Yung, 2016. "Linear-Quadratic Mean Field Games," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 496-529, May.
    2. Ivar Ekeland & Delphine Lautier & Bertrand Villeneuve, 2019. "Hedging pressure and speculation in commodity markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(1), pages 83-123, July.
    3. Hirshleifer, David, 1990. "Hedging Pressure and Futures Price Movements in a General Equilibrium Model," Econometrica, Econometric Society, vol. 58(2), pages 411-428, March.
    4. William Lefebvre & Gregoire Loeper & Huy^en Pham, 2020. "Mean-variance portfolio selection with tracking error penalization," Papers 2009.08214, arXiv.org, revised Sep 2020.
    5. Hirshleifer, David, 1988. "Risk, Futures Pricing, and the Organization of Production in Commodity Markets," Journal of Political Economy, University of Chicago Press, vol. 96(6), pages 1206-1220, December.
    6. Benth, Fred Espen & Cartea, Álvaro & Kiesel, Rüdiger, 2008. "Pricing forward contracts in power markets by the certainty equivalence principle: Explaining the sign of the market risk premium," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2006-2021, October.
    7. Ing-Haw Cheng & Wei Xiong, 2014. "Why Do Hedgers Trade So Much?," The Journal of Legal Studies, University of Chicago Press, vol. 43(S2), pages 183-207.
    8. Frans A. De Roon & Theo E. Nijman & Chris Veld, 2000. "Hedging Pressure Effects in Futures Markets," Journal of Finance, American Finance Association, vol. 55(3), pages 1437-1456, June.
    9. Ren'e Aid & Giorgia Callegaro & Luciano Campi, 2019. "No-Arbitrage Commodity Option Pricing with Market Manipulation," Papers 1909.07896, arXiv.org, revised Mar 2020.
    10. Amine Ismail & Huyên Pham, 2019. "Robust Markowitz mean‐variance portfolio selection under ambiguous covariance matrix," Mathematical Finance, Wiley Blackwell, vol. 29(1), pages 174-207, January.
    11. Allaz, Blaise, 1992. "Oligopoly, uncertainty and strategic forward transactions," International Journal of Industrial Organization, Elsevier, vol. 10(2), pages 297-308, June.
    12. René Aïd & Matteo Basei & Huyên Pham, 2020. "A McKean–Vlasov approach to distributed electricity generation development," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(2), pages 269-310, April.
    13. Blaise Allaz, 1992. "Oligopoly, uncertainty and strategic forward transactions," Post-Print hal-00511812, HAL.
    14. David Hirshleifer, 1988. "Residual Risk, Trading Costs, and Commodity Futures Risk Premia," Review of Financial Studies, Society for Financial Studies, vol. 1(2), pages 173-193.
    15. Matteo Basei & Huyên Pham, 2019. "A Weak Martingale Approach to Linear-Quadratic McKean–Vlasov Stochastic Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 347-382, May.
    16. Blaise Allaz & Jean-Luc Vila, 1993. "Cournot Competition, Forward Markets and Efficiency," Post-Print hal-00511806, HAL.
    17. Aïd, René & Callegaro, Giorgia & Campi, Luciano, 2020. "No-arbitrage commodity option pricing with market manipulation," LSE Research Online Documents on Economics 103815, London School of Economics and Political Science, LSE Library.
    18. Willliam Lefebvre & Gregoire Loeper & Huyên Pham, 2020. "Mean-variance portfolio selection with tracking error penalization," Working Papers hal-02941289, HAL.
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