Application of discrete and continous time Models in valuation of credit insurance for Asset-based lending companies

Abstract

Asset-based lending companies and other loan providers are exposed to risk of loan defaults by borrowers. To reduce this risk, these companies acquire credit insurance. Thus when the borrower defaults in payment, the insurance company covers a percentage of the outstanding balance which generates a way to lessen and spread credit risk that the lender incurs. Therefore there are a number of methods put in place such as frequency-severity and hazard rate models used to value credit insurance. Valuing of credit insurance for asset-based lending companies is a challenging task especially in Kenyan market, where in the case of a borrower's default, the process for recovering of the collateral will last a longer period of more than a year and where data on the borrower's behavior of payment is of poor quality or generally unavailable. The existing methods do not consider the time to repossession of the collateral in case of loan default. Our proposed model takes into account time to repossession of the collateral and can be used in emerging market economies where other available methods may be either unsuitable or are too complex to implement due to lack of enough data. Therefore, this project aims to incorporate the discrete and continuous time models to forecast loss reserves in credit insurance for asset-based lending companies. First, we established a discrete-time model to describe delinquency of credits in loan insurance product. Martingale properties, Replicating of asset portfolio strategy and Ito's calculus are used to obtain results on expected values of future losses of credit insurance products. Secondly, we used the Black-Scholes model to develop a continuous-time model to forecast future losses in credit insurances. This is constructed by linking it from the discrete-time model using the methods of stochastic calculus. We estimated the loss reserves by first applying the Geometric Brownian Motion simulation to predict the probability of default of the borrower. The probability of default was then multiplied by the simulated outstanding balances, a factor that considers the time to repossession of the collateral and the assumed percentage coverage of the insurance company to obtain estimates of loss reserves in credit insurance.