Valuation of surrender option using Crank-Nicolson and Hopscotch methods
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Date
NOVEMBER, 2015
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Abstract
Most of the insurance contracts in Ghana contains the right to early termination
and are also path-depend, due to the presence of path-dependence derivatives
and the right to early termination of the contract, can make valuation of Life
insurance contract in Ghana come with complexities. These complexities are
aggravated with introduction of the new parameter (S). Termination of life
insurance contract in Ghana among other factors may come as a result of many
factors that policyholders face. This study seeks to modify the Black-Scholes
partial differential equation by incorporating risk of being multimorbid, and
investigate the suitability of using some existing numerical methods (Crank-
Nicolson and Hopscotch) to value life insurance contract. Further comparison
between the two methods were done to select an efficient method for the modified
model. In line with these objectives, simulations for time of an individual
to be multimorbid were performed and the survival for risk of multimorbidity
computed. This study revealed that, the modified model is stable, consistent and
hence suitable to solve. In the numerical analysis of the option valuation using
the original Black-Scholes model, Crank-Nicolson method converges faster than
Hopscotch method. On the other hand, numerical analysis of the option valuation
using the Black-Scholes model with the incorporated multi-morbid survival rate,
Hopscotch method converges faster than Crank-Nicolson method. Further, it
is observed that, the Hopscotch method converges much faster and give higher
values as the step sizes are increased for Black-Scholes partial differential equation
of the life insurance contract in Ghana embedded with surrender option. Hence,
making the Hopscotch method favour policyholders who might want to surrender
in order to receive the surrender value (payoffs).
Description
A thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology in partial fulfillment of the requirement for the degree of Master of Philosophy in Acturial Science.