Glover, E. N. (2009) Analytic pricing of American put options. Masters thesis, Rhodes University.

Text
GloverMScTR0917.pdf 659Kb 
Abstract
American options are the most commonly traded financial derivatives in the market. Pricing these options fairly, so as to avoid arbitrage, is of paramount importance. Closed form solutions for American put options cannot be utilised in practice and so numerical techniques are employed. This thesis looks at the work done by other researchers to find an analytic solution to the American put option pricing problem and suggests a practical method, that uses Monte Carlo simulation, to approximate the American put option price. The theory behind option pricing is first discussed using a discrete model. Once the concepts of arbitragefree pricing and hedging have been dealt with, this model is extended to a continuoustime setting. Martingale theory is introduced to put the option pricing theory in a more formal framework. The construction of a hedging portfolio is discussed in detail and it is shown how financial derivatives are priced according to a unique riskneutral probability measure. BlackScholes model is discussed and utilised to find closed form solutions to European style options. American options are discussed in detail and it is shown that under certain conditions, American style options can be solved according to closed form solutions. Various numerical techniques are presented to approximate the true American put option price. Chief among these methods is the Richardson extrapolation on a sequence of Bermudan options method that was developed by Geske and Johnson. This model is extended to a RepeatedRichardson extrapolation technique. Finally, a Monte Carlo simulation is used to approximate Bermudan put options. These values are then extrapolated to approximate the price of an American put option. The use of extrapolation techniques was hampered by the presence of nonuniform convergence of the Bermudan put option sequence. When convergence was uniform, the approximations were accurate up to a few cents difference.
Item Type:  Thesis (Masters) 

Uncontrolled Keywords:  Itô Stochastic Calculus; BlackSchotes; American & Bermudan Options; Derivative securities 
Subjects:  Q Science > QA Mathematics > QA273 Probabilities. Mathematical statistics 
Divisions:  Faculty > Faculty of Commerce > Statistics Faculty > Faculty of Science > Statistics 
Supervisors:  Szyszkowski, I. (Prof.) 
ID Code:  1606 
Deposited By:  Nicolene Mvinjelwa 
Deposited On:  26 Apr 2010 10:04 
Last Modified:  06 Jan 2012 16:21 
177 fulltext download(s) in the past 12 months
More statistics...
Repository Staff Only: item control page