Tailored Car Lease Contract Based on Stochastic Process

In a leasing contract, a buyer pays a monthly fee to the lender for utilizing a non-consumable commodity over a given period. The monthly leasing payment depends upon the residual value at the end of the contract estimated by the lender. Therefore, the estimation of the residual value can impact the resale value of the commodity, customer attrition rate, and the firm's market competitiveness. The value of the commodity is stochastic, depending on the usage of the vehicle and accidents. The change in the value is modeled by a mean-reverting process--the Ornstein-Uhlenbeck process--which is represented by a binomial lattice. The leasing contract is tailored considering several real-world scenarios, such as accident during the lease term, trade-in for another car before lease expiry, and hand over the car after lease maturity. Based on the presented scenarios, the best offer is made to the customer to minimize the risk of the lender.