Convertible lease risk spread modeling with correlation

The purpose of this paper is to model the spread between risky and risk-free convertible lease arrangements allowing for correlation between the unexpected changes of firm’s cash flow and service flow of the leased asset and considering lessee’s financial soundness, lessor’s risk premium requirements as well as economic uncertainty. The lease risk spread is modeled for two types of convertible leases, namely the convertible lease based on service flow (CLSF) and the convertible lease based on rental payment (CLRP). The difference between both types of contracts lies in the conversion basis when assessing the remaining unpaid payments. The CLSF uses the service flows of the leased asset while the CLRP uses the contractual fee initially due. The numerical analysis revealed that correlation is the most relevant parameter in the variance of uncertainty and consequently in the magnitude and sign of the convertible lease risk spread values for both types of contracts. Additionally, it was found that the higher the uncertainty, the higher the spread value, suggesting that the variance of uncertainty plays a central role in the lessee's probability of default calculation. Moreover, the spread of the CLSF (CLSSF) is higher than that of the CLRP (CLSRP) referring to the triggering conversion basis which is random in the first contract and fixed in the second.