The Black-Scholes model and its assumptions has endured its fair share of criticism.
One problematic issue is the model’s assumption that market volatility is constant.
The past decade has seen numerous publications addressing this issue by adapting the
Black-Scholes model to incorporate stochastic volatility. In this dissertation, American
put options are priced under the Heston stochastic volatility model using the Crank-
Nicolson finite difference method in combination with the Projected Over-Relaxation
method (PSOR). Due to the early exercise facility, the pricing of American put options
is a challenging task, even under constant volatility. Therefore the pricing problem under
constant volatility is also included in this dissertation. It involves transforming the
Black-Scholes partial differential equation into the heat equation and re-writing the pricing
problem as a linear complementary problem. This linear complimentary problem is
solved using the Crank-Nicolson finite difference method in combination with the Projected
Over-Relaxation method (PSOR). The basic principles to develop the methods
necessary to price American put options are covered and the necessary numerical methods
are derived. Detailed algorithms for both the constant and the stochastic volatility
models, of which no real evidence could be found in literature, are also included in this
dissertation. / MSc (Applied Mathematics), North-West University, Potchefstroom Campus, 2013
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:nwu/oai:dspace.nwu.ac.za:10394/10202 |
| Date | January 2013 |
| Creators | Joubert, Dominique |
| Publisher | North-West University |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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