Theorem 1: In general, the value of the pledged assets V, the risk-free rate r, the maturity date of the fixed-rate zero-coupon loans T, the current time t, the loan rate R, and the volatility of the pledged assets determine the pledged loan-to-value ratio.
Therefore, our core research problem is to determine the pledged loan-to-value ratio under the premise of reasonable pricing, which means solving the inverse problem of similar foreign research.
This is the determining equation of the pledged loan-to-value ratio x.
(12 Because N x) + N(−x) = 1, we can obtain the determining equation of the pledged loan-to-value ratio.
Thus, through step-by-step derivation, we can get the value of the loan and the determining equation of the pledged loan-to-value ratio at any moment.
Proof of theorem 7: The determining equation of the pledged loan-to-value ratio is as follows: frac{Rx}{r}V 0)+frac{Rx}{r}V(0)left(frac{1}{theta_-1}right){lefrac{V}{overline{V}}rightght)}^{theta_=xV.
The determining equation of the pledged loan-to-value ratio is as follows: xV t){e}^{left R-rright tau }-varPhi left(x,V(t),R,T,tright)=xV(t) (5).
The ninth paper, "Determining pledged loan-to-value ratio: an option pricing perspective", by Ran Zhang, Jing Zhang, and Shuang Xu, investigates the determination of the pledged loan-to-value ratio in an option pricing environment and mainly articulated the theoretical framework and analytical method.
First, each different loan term has its own pledged loan-to-value ratio, thus this method allows us to determine the term structure of the pledged loan-to-value ratio.
Theorem 6: If the price of the pledged property follows a geometric Brownian motion, the determining equation of the pledged loan-to-value ratio is as follows: {e}^{ktau }Nleft({d}_2right)=1-frac{1}{x}Nleft -{d}_1right), (13)where d i, i =1-frac{1}{x}Nleft -{dquation (12).
