An Algorithm for the Pricing and Timing of the Option to Make a Two-stage Investment with Credit Guarantees

31 Pages Posted: 12 Apr 2021 Last revised: 8 Nov 2021

See all articles by Linjia Dong

Linjia Dong

Southern University of Science and Technology; Harbin Institute of Technology

Zhaojun Yang

Southern University of Science and Technology - Department of Finance

Date Written: April 15, 2021

Abstract

We develop a jump-diffution model for a guarantee-investment combination financing mode (G-I mode) that is recently popular in financial practice. We assume that a borrower has exclusively an option to invest in a project in two stages. The project's cash flow follows a double exponential jump-diffusion process and it is increased by a growth factor once the second-stage investment is exercised. The first-stage investment cost is financed by a bank loan with the guarantee provided by an insurer, who promises to provide the second-stage investment cost as well as take the lender's all default losses. In return for the guarantee and investment, the borrower pays a guarantee fee upon first investment and grants a fraction of equity upon second investment to the insurer. In sharp contrast to prior papers on guarantee, the guarantee costs are contracted prior to investment. We provide closed-form solutions and produce a numerical algorithm for the timing and pricing of the two investment options.

Keywords: Entrepreneurship; Guarantee-Investment mode; Growth options; Jump-diffusion; Algorithm

JEL Classification: G12; H81; G31

Suggested Citation

Dong, Linjia and Yang, Zhaojun, An Algorithm for the Pricing and Timing of the Option to Make a Two-stage Investment with Credit Guarantees (April 15, 2021). Available at SSRN: https://ssrn.com/abstract=3822814 or http://dx.doi.org/10.2139/ssrn.3822814

Linjia Dong

Southern University of Science and Technology ( email )

1088 Xueyuan Avenue
Shenzhen, Guangdong 518055
China

Harbin Institute of Technology ( email )

92 Xidazhi Street
Harbin, 150001
China

Zhaojun Yang (Contact Author)

Southern University of Science and Technology - Department of Finance ( email )

No 1088, Xueyuan Rd.
District of Nanshan
Shenzhen, Guangdong 518055
China

HOME PAGE: http://faculty.sustc.edu.cn/profiles/yangzj

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