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

Ran Zhang (), Jing Zhang and Shuang Xu
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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

Financial Innovation, 2015, vol. 1, issue 1, 1-13

Abstract: 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.

Keywords: Pledged loan; Loan-to-value ratio; Put option; Term structure of pledged ratio; Value volatility of pledge (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1186/s40854-015-0015-4

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