Investment and Financing for SMEs with a Partial Guarantee and Jump Risk

Abstract

Many SMEs and young entrepreneurs experience financing constraints due to their low credibility and information asymmetry. To this end, a partial guarantee agreement is popular with Chinese entrepreneurs. In this paper, we consider an SME with a funding gap, who wants to invest in a project, of which the cash flow follows a double exponential jump-diffusion process. In contrast to traditional corporate finance theory, we assume the SME is unable to get loan directly from banks because of its high project risk, strong information asymmetry and low credibility of SMEs. To overcome such financing constraints, the SME turns to an insurer and enters into a partial guarantee agreement, where a bank lends cash to the SME with the insurer promising to undertake a fraction (guarantee level) of debt once the SME defaults. In return, the SME (borrower) allocates a fraction of equity and a fixed guarantee fee rate per unit time to the insurer. We assume the investment is irreversible and can be postponed. Utilizing a real options approach, we develop an investment and financing model with the partial guarantee. We explicitly derive the pricing and timing of the option to invest for the cash flow with both diffusion and jump risk. The two sources of project risk increase the value of the option and postpone investment. More importantly, we reveal that larger funding gaps or higher guarantee levels lead to a later investment and generally a slightly less value of the option to invest. Interestingly, raising the guarantee level can effectively reduce the borrower's moral hazard to increase equity values at the expense of the lender. Meanwhile, an increase in the guarantee level does not add disincentive for the SME to replenish its equity.

Keywords: Guarantee level, Investment and financing, Real options, Double exponential jump-diffusion process

JEL Classification: G11, G32