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Stock loan with Automatic termination clause, cap and margin

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  • Shuqing Jiang
  • Zongxia Liang
  • Weiming Wu

Abstract

This paper works out fair values of stock loan model with automatic termination clause, cap and margin. This stock loan is treated as a generalized perpetual American option with possibly negative interest rate and some constraints. Since it helps a bank to control the risk, the banks charge less service fees compared to stock loans without any constraints. The automatic termination clause, cap and margin are in fact a stop order set by the bank. Mathematically, it is a kind of optimal stopping problems arising from the pricing of financial products which is first revealed. We aim at establishing explicitly the value of such a loan and ranges of fair values of key parameters : this loan size, interest rate, cap, margin and fee for providing such a service and quantity of this automatic termination clause and relationships among these parameters as well as the optimal exercise times. We present numerical results and make analysis about the model parameters and how they impact on value of stock loan.

Suggested Citation

  • Shuqing Jiang & Zongxia Liang & Weiming Wu, 2010. "Stock loan with Automatic termination clause, cap and margin," Papers 1005.1357, arXiv.org, revised Sep 2010.
    • Handle: RePEc:arx:papers:1005.1357
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    References listed on IDEAS

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    1. Hans U. Gerber & Hlias S. W. Shiu, 1996. "Martingale Approach To Pricing Perpetual American Options On Two Stocks," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 303-322, July.
    2. Min Dai & Yue Kuen Kwok & Lixin Wu, 2004. "Optimal Shouting Policies Of Options With Strike Reset Right," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 383-401, July.
    3. Windcliff, H. & Forsyth, P. A. & Vetzal, K. R., 2001. "Valuation of segregated funds: shout options with maturity extensions," Insurance: Mathematics and Economics, Elsevier, vol. 29(1), pages 1-21, August.
    4. Andreas Kyprianou, 2004. "Some calculations for Israeli options," Finance and Stochastics, Springer, vol. 8(1), pages 73-86, January.
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    Cited by:

    1. Minh-Quan Nguyen & Nhat-Tan Le & Khuong Nguyen-An & Duc-Thi Luu, 2024. "An Integral Equation Approach for the Valuation of Finite-maturity margin-call Stock Loans," Papers 2407.14728, arXiv.org.
    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).

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