Pricing of Margin Call Stock Loan Based on the FMLS

Kaili Xiang,Xiao Li,Peng Hu

doi:10.1155/2020/5349345

Abstract

In common stock loan, lenders face the risk that their loans will not be repaid if the stock price falls below loan, which limits the issuance and circulation of stock loans. The empirical test suggests that the log-return series of stock price in the US market reject the normal distribution and admit instead a subclass of the asymmetric distribution. In this paper, we investigate the model of the margin call stock loan problem under the assumption that the return of stock follows the finite moment log-stable process (FMLS). In this case, the pricing model of the margin call stock loan can be described by a space-fractional partial differential equation with a time-varying free boundary condition. We transform the free boundary problem to a linear complementarity problem, and the fully-implicit finite difference method that we used is unconditionally stable in both the integer and fractional order. The numerical experiments are carried out to demonstrate differences of the margin call stock loan model under the FMLS and the standard normal distribution. Last, we analyze the impact of key parameters in our model on the margin call stock loan evaluation and give some reasonable explanation.

Highlights

Stock loan is a contract that the holders of securities take these securities as collateral to obtain loans from commercial banks
We found that the higher the loan interest rate c is, the lower the contract value of the margin call stock loan is because in practice, the higher the loan interest rate is, the higher the interest the borrower needs to pay and the faster the barrier
It can be seen from the figure that the margin call stock loan increases with the volatility σ because the nonrecourse stock loan is similar to an American option

Summary

Introduction

Stock loan is a contract that the holders of securities take these securities as collateral to obtain loans from commercial banks. According to the above assumptions, the partial differential equation and boundary conditions of the pricing of the margin call stock loan can be obtained as zVmc(x, zt t) rVmc(x, t). The partial differential equations and boundary conditions of the nonrecourse stock loan pricing with variable strike price under the framework of FMLS are as follows:. We derive the partial differential equations and boundary conditions for pricing contracts with recourse under the framework of FMLS, where the lower boundary is relatively special due to the limitation of recourse. We will use the finite difference scheme to give the numerical solution of equation (12)

Numerical Format of the Model

Numerical Example

Conclusion