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Determining pledged loan-to-value ratio: an option pricing perspective

Author

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  • Ran Zhang

    (University of Science and Technology Beijing)

  • Jing Zhang

    (University of Science and Technology Beijing)

  • Shuang Xu

    (University of Science and Technology Beijing)

Abstract

Background We investigated the determination of the pledged loan-to-value ratio in an optionpricing environment and mainly articulated the theoretical framework and analytical method. Methods The basic idea is that the present value of the pledged loan payoff is equal to a put option’s value.While the interest rate is fixed and the loan is without coupon, we analyzed the pledged loan-to-value ratioin the option pricing perspective and got it that the pledged loan-to-value ratio is decided by term, excessreturn, and the value volatility of the pledge. Next, we extended the same work to coupon loan and portfoliopledge circumstances. For zero coupon and fixed interest rate circumstances, we performed a numericalanalysis. Results Our results indicate the following:the pledged loan-to-value ratio is a convex decreasing function ofthe term; and the pledged loan-to-value ratio is a concave decreasing function of the value volatility of the pledge; and the pledged loan-to-value ratio is a concave increasing function of the risk premium. For floating interest rate circumstances, we should specify the function form between the loan interest and the risk-free rate. Conclusions The scientific measurement of the pledged loan-to-value ratio means that simple rules of thumb or the VaR method may lead to mispricing, which could create the possibility of arbitrage. In this way, a new direction for trading derivative products of pledges will be provided.

Suggested Citation

  • Ran Zhang & Jing Zhang & Shuang Xu, 2015. "Determining pledged loan-to-value ratio: an option pricing perspective," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 1(1), pages 1-13, December.
    • Handle: RePEc:spr:fininn:v:1:y:2015:i:1:d:10.1186_s40854-015-0015-4
    DOI: 10.1186/s40854-015-0015-4
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    References listed on IDEAS

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    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    2. Robert A. Jarrow & David Lando & Stuart M. Turnbull, 2008. "A Markov Model for the Term Structure of Credit Risk Spreads," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 18, pages 411-453, World Scientific Publishing Co. Pte. Ltd..
    3. Robert A. Jarrow & Stuart M. Turnbull, 2008. "Pricing Derivatives on Financial Securities Subject to Credit Risk," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 17, pages 377-409, World Scientific Publishing Co. Pte. Ltd..
    4. repec:bla:ecnote:v:32:y:2003:i:2:p:243-282 is not listed on IDEAS
    5. Postali, Fernando A.S. & Picchetti, Paulo, 2006. "Geometric Brownian Motion and structural breaks in oil prices: A quantitative analysis," Energy Economics, Elsevier, vol. 28(4), pages 506-522, July.
    6. Ono, Arito & Uchida, Hirofumi & Udell, Gregory & Uesugi, Iichiro, 2013. "A Close Look at Loan-To-Value Ratios: Evidence from the Japanese Real Estate Market," Working Paper Series 19, Center for Interfirm Network, Institute of Economic Research, Hitotsubashi University.
    7. Alvarez-Ramirez, Jose & Alvarez, Jesus & Rodriguez, Eduardo, 2008. "Short-term predictability of crude oil markets: A detrended fluctuation analysis approach," Energy Economics, Elsevier, vol. 30(5), pages 2645-2656, September.
    8. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    9. Cossin, Didier & González, Fernando & Huang, Zhijiang & Backé, Peter, 2003. "A framework for collateral risk control determination," Working Paper Series 209, European Central Bank.
    10. Esa Jokivuolle & Samu Peura, 2003. "Incorporating Collateral Value Uncertainty in Loss Given Default Estimates and Loan‐to‐value Ratios," European Financial Management, European Financial Management Association, vol. 9(3), pages 299-314, September.
    11. Stulz, ReneM. & Johnson, Herb, 1985. "An analysis of secured debt," Journal of Financial Economics, Elsevier, vol. 14(4), pages 501-521, December.
    12. John A. Buzacott & Rachel Q. Zhang, 2004. "Inventory Management with Asset-Based Financing," Management Science, INFORMS, vol. 50(9), pages 1274-1292, September.
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    Cited by:

    1. Jenny Jing Wang & Jianfu Shen & Frederik Pretorius, 2023. "Valuing options to renew at future market value: the case of commercial property leases," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-35, December.

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