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

We develop a jump-diffusion 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-diffu...

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Bibliographic Details
Published in:Computational economics 2022-10, Vol.60 (3), p.1175-1196
Main Authors: Dong, Linjia, Yang, Zhaojun
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Bank loans
Banks (Finance)
Behavioral/Experimental Economics
Cash flow
Computer Appl. in Social and Behavioral Sciences
Credit
Diffusion
Economic aspects
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Economics and Finance
Equity
Financing
Grants
Growth factors
Guarantees
Investments
Math Applications in Computer Science
Numerical analysis
Operations Research/Decision Theory
Pricing
Swaps (Finance)
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Summary:We develop a jump-diffusion 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.
ISSN:0927-7099
1572-9974
DOI:10.1007/s10614-021-10220-8