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Self-financing strategy expression in general shape limit order book with market impacts in continuous time

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  • Taiga Saito

    (Financial Research Center at Financial Services Agency, Government of Japan, 3-2-1 Kasumigaseki, Chiyoda-ku, Tokyo 100-8967, Japan)

Abstract

In this paper, we extend the self-financing strategy expression in the linear supply curve model with market impacts by Roch (2011) and Cetin et al. (2004) to a non-linear case. Option hedging with liquidity costs and market impacts has been a key issue since the financial crises. We generalize the continuous time expression of a self-financing strategy in the linear supply curve model with market impacts proposed by Roch (2011) and Cetin et al. (2004), which is a useful result when one considers an option hedging strategy under an illiquid market, to a non-linear case. After showing an expression of the maximum price to when a hedger buys a certain amount under the non-linear supply curve, we define a non-linear market impact and show the self-financing expression under the non-linear supply curve model with market impacts. We also show examples of the strategy in non-linear supply curves observed in practice.

Suggested Citation

  • Taiga Saito, 2015. "Self-financing strategy expression in general shape limit order book with market impacts in continuous time," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(03), pages 1-19.
    • Handle: RePEc:wsi:ijfexx:v:02:y:2015:i:03:n:s2424786315500346
    DOI: 10.1142/S2424786315500346
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    Cited by:

    1. Ahmet Umur Ozsoy & Omur Uu{g}ur, 2023. "The QLBS Model within the presence of feedback loops through the impacts of a large trader," Papers 2311.06790, arXiv.org.
    2. Taiga Saito, 2017. "Hedging and pricing illiquid options with market impacts," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-37, June.

    More about this item

    Keywords

    Liquidity risk; self-financing trading strategy; market impacts; D40; G13;
    All these keywords.

    JEL classification:

    • D40 - Microeconomics - - Market Structure, Pricing, and Design - - - General
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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