DERIVATION OF A STOCHASTIC LOAN REPAYMENT MODEL FOR VALUING A REVENUE-BASED LOAN CONTRACT

Hassan Mazengera ()
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Hassan Mazengera: Department of Statistics, Rhodes University, Grahamstown 6140, South Africa

Annals of Financial Economics (AFE), 2017, vol. 12, issue 03, 1-29

Abstract: In this paper, we derive a stochastic loan repayment model, that will be used to quantify or ascertain the maximum borrowing capacity for a firm. Initially, we derived the revenue and then the stochastic loan repayment model. The derived stochastic loan repayment model is a function of the generated revenue. We also show that the model is consistent with our expectations, that is α, the proportion of revenue that goes toward loan repayment is a very important parameter as far as ascertaining default is concerned. Under stochastic loan repayment model, a firm will be highly likely to default the moment α which approaches one. Technically, this means that all the revenue is used in loan repayment. Finally, we show that when financial institutions lend using the fixed repayment regime, fixed periodic installments must be less than or equal to stochastic repayment amount, otherwise there will be a default. From this analysis, we ended up with a very crucial boundary relationship between the loan amount, L and the stochastic loan repayment amount. The derived stochastic loan repayment model works well in a less volatile environment. When volatility exceeds 100%, we may need more frequent revenue values to achieve the desired results.

Keywords: Stochastic loan repayment; risk-neutral valuation; loan loss reserve; stochastic differential equation; revenue-based lending; default (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1142/S2010495217500130

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