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Teka, Kubrom Hisho 2013-04-26T20:56:43Z 2013-04-26T20:56:43Z 2013-04-26 2013 May http://hdl.handle.net/2097/15669 In financial mathematics, asset prices for European options are often modeled according to the Black-Scholes-Merton (BSM) model, a stochastic differential equation (SDE) depending on unknown parameters. A derivation of the solution to this SDE is reviewed, resulting in a stochastic process called geometric Brownian motion (GBM) which depends on two unknown real parameters referred to as the drift and volatility. For additional insight, the BSM equation is expressed as a heat equation, which is a partial differential equation (PDE) with well-known properties. For American options, it is established that asset value can be characterized as the solution to an obstacle problem, which is an example of a free boundary PDE problem. One approach for estimating the parameters in the GBM solution to the BSM model can be based on the method of maximum likelihood. This approach is discussed and applied to a dataset involving the weekly closing prices for the Dow Jones Industrial Average between January 2012 and December 2012. Master of Science Masters Department of Statistics James W. Neill en_US Kansas State University © the author. This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). http://rightsstatements.org/vocab/InC/1.0/ Parameter estimation Black-Scholes-Merton model Statistics (0463) Parameter estimation of the Black-Scholes-Merton model Report open.access