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Stock Loans in Incomplete Markets

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  • Matheus R. Grasselli
  • Cesar Gómez

Abstract

A stock loan is a contract whereby a stockholder uses shares as collateral to borrow money from a bank or financial institution. In Xia and Zhou (2007, Stock loans, Mathematical Finance, 17(2), pp. 307--317), this contract is modelled as a perpetual American option with a time-varying strike and analysed in detail within a risk-neutral framework. In this paper, we extend the valuation of such loans to an incomplete market setting, which takes into account the natural trading restrictions faced by the client. When the maturity of the loan is infinite, we use a time-homogeneous utility maximization problem to obtain an exact formula for the value of the loan fee to be charged by the bank. For loans of finite maturity, we characterize the fee using variational inequality techniques. In both cases, we show analytically how the fee varies with the model parameters and illustrate the results numerically.

Suggested Citation

  • Matheus R. Grasselli & Cesar Gómez, 2013. "Stock Loans in Incomplete Markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 20(2), pages 118-136, April.
    • Handle: RePEc:taf:apmtfi:v:20:y:2013:i:2:p:118-136
    DOI: 10.1080/1350486X.2012.660318
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    Cited by:

    1. McWalter, Thomas A. & Ritchken, Peter H., 2022. "Black economic empowerment regulation and risk incentives," Journal of Economic Dynamics and Control, Elsevier, vol. 139(C).
    2. Kristoffer Glover & Hardy Hulley, 2022. "Short Selling With Margin Risk And Recall Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 25(02), pages 1-33, March.
    3. McWalter, Thomas A. & Ritchken, Peter H., 2022. "On stock-based loans," Journal of Financial Intermediation, Elsevier, vol. 52(C).
    4. Lukasz Szpruch & Marc Sabat'e Vidales & Tanut Treetanthiploet & Yufei Zhang, 2024. "Pricing and hedging of decentralised lending contracts," Papers 2409.04233, arXiv.org.

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