Numerical valuation of surrender options
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Date
2016-03-23
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Abstract
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. In Ghana, poverty levels coupled with social burdens can inform
a multi-morbid person to surrender a life policy contract. The study seeks to
incorporate the multi-morbid survival rate of a policy holder in the Black-Scholes
model for option pricing. The solution to this model come along 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 algorithms
in solving the proposed Black-Scholes equation ;the Crank-Nicolson method and
the Implicit method. In line with these objectives, simulations of survival times
were performed to compute the survival rate and the stability, consistency and
convergence of these algorithms were investigated. It was observed that the
algorithms were stable, consistent and converges to the exact solution. However the
Explicit method of the finite difference approximation is found to be conditionally
stable. Numerical solution to the Black -Scholes model and the proposed model
indicates that the Crank-Nicolson method converges faster than the Implicit method
for the Black-Scholes while the Implicit method converges faster than the Crank-
Nicolson method. Finally it is observed that the Implicit method converges faster as
the multi-morbid survival rate decreases below the short rate of the Black-Scholes
model.
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 Actuarial Science, 2015