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The Black Scholes Model (1973) is used to price and hedge plain vanilla barrier options on a non dividend paying asset.
Under this model, Monte Carlo Simulation, Stratified sampling, Simpson’s rule, Trapezoidal rule and Antithetic variable techniques have been used to determine the value and hedging portfolio of a plain vanilla barrier option.
Also stochastic dynamic programming has been developed so as to determine the price and hedging portfolio of the option.
Finally the methods are compared to each other in terms of accuracy.
It is found that stratified sampling technique is the best method after comparing with other methods.
Emmanuel Deogratias is a graduate holding BED(Mathematics)from the University of Dar es Salaam, Tanzania and MSc (Mathematical Modeling) from the same university obtained in 2008 and 2011 respectively.He joined the University of Dodoma, Tanzania in January, 2009 as Tutorial assistant in Mathematics Department.Currently,he is Assistant Lecturer
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