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A model for a large investor trading at market indifference prices. I: Single-period case

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  • Peter Bank
  • Dmitry Kramkov

Abstract

We develop a single-period model for a large economic agent who trades with market makers at their utility indifference prices. We compute the sensitivities of these market indifference prices with respect to the size of the investor’s order. It turns out that the price impact of an order is determined both by the market makers’ joint risk tolerance and by the variation of individual risk tolerances. On a technical level, a key role in our analysis is played by a pair of conjugate saddle functions associated with the description of Pareto optimal allocations in terms of the aggregate utility function. Copyright Springer-Verlag Berlin Heidelberg 2015

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  • Peter Bank & Dmitry Kramkov, 2015. "A model for a large investor trading at market indifference prices. I: Single-period case," Finance and Stochastics, Springer, vol. 19(2), pages 449-472, April.
    • Handle: RePEc:spr:finsto:v:19:y:2015:i:2:p:449-472
    DOI: 10.1007/s00780-015-0258-y
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    Cited by:

    1. Ibrahim Ekren & Sergey Nadtochiy, 2019. "Utility-based pricing and hedging of contingent claims in Almgren-Chriss model with temporary price impact," Papers 1910.01778, arXiv.org, revised Jun 2020.
    2. Roxana Dumitrescu & Marie-Claire Quenez & Agn`es Sulem, 2017. "American options in an imperfect market with default," Papers 1708.08675, arXiv.org.
    3. Michail Anthropelos & Scott Robertson & Konstantinos Spiliopoulos, 2021. "Optimal investment, derivative demand, and arbitrage under price impact," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 3-35, January.
    4. Thai Nguyen & Mitja Stadje, 2020. "Utility maximization under endogenous pricing," Papers 2005.04312, arXiv.org, revised Mar 2024.
    5. Miryana Grigorova & Marie-Claire Quenez & Agnès Sulem, 2019. "European options in a non-linear incomplete market model with default," Working Papers hal-02025833, HAL.
    6. Miryana Grigorova & Marie-Claire Quenez & Agnès Sulem, 2020. "European options in a non-linear incomplete market model with default," Post-Print hal-02025833, HAL.
    7. Grigorova, Miryana & Quenez, Marie-Claire & Sulem, Agnès, 2021. "American options in a non-linear incomplete market model with default," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 479-512.
    8. Miryana Grigorova & Marie-Claire Quenez & Agnès Sulem, 2019. "American options in a non-linear incomplete market model with default," Working Papers hal-02025835, HAL.
    9. Miryana Grigorova & Marie-Claire Quenez & Agnès Sulem, 2021. "American options in a non-linear incomplete market model with default," Post-Print hal-02025835, HAL.
    10. Peter Bank & Selim Gökay, 2016. "Superreplication when trading at market indifference prices," Finance and Stochastics, Springer, vol. 20(1), pages 153-182, January.
    11. Masaaki Fukasawa & Mitja Stadje, 2018. "Perfect hedging under endogenous permanent market impacts," Finance and Stochastics, Springer, vol. 22(2), pages 417-442, April.

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    More about this item

    Keywords

    Aggregate utility function; Bertrand competition; Demand pressure; Equilibrium; Large investor; Liquidity; Pareto allocation; Price impact; Risk tolerance; Utility indifference prices; 52A41; 60G60; 91G10; 91G20; G11; G12; G13; C61;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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