Journal of Advances in Mathematics and Computer Science

Embedded in Life insurance contracts are surrender options and also path dependency. Surrender option stems from many reasons. Multi-morbidity increases the rate of mortality and a variety of adverse health outcomes which may lead to surrendering. Poverty levels coupled with social burdens can inform a multi-morbid person to surrender a life policy contract. The study seeks determine and compare valuation of options of a multi-morbid person surrendering. In line with this objective the multi-morbid survival rate of a policy holder was incorporated in the Black- Scholes model for option pricing. The solution to the model come with its own complexities, therefore the need to resort to numerical solutions for the option valuation. Further, a comparison is made of two finite difference algorithm in solving the proposed Black-Scholes equation; the Crank-Nicolson method and the Hopscotch method. Simulations of survival were performed tocompute the survival rate. Numerical solution to the Black-Scholes model and the proposed model indicates that the Crank-Nicolson method converges faster than the Hopscotch method for the Black-Scholes whiles the Hopscotch method converges faster than the Crank-Nicolson for the proposed modified Black-Scholes model. It was observed that the Hopscotch method converges faster as the multi-morbid survival rate decreases below the short rate of the Black-Scholes model.