Parameter estimation of the Black-Scholes-Merton model

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dc.contributor.author Teka, Kubrom Hisho
dc.date.accessioned 2013-04-26T20:56:43Z
dc.date.available 2013-04-26T20:56:43Z
dc.date.issued 2013-04-26
dc.identifier.uri http://hdl.handle.net/2097/15669
dc.description.abstract 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. en_US
dc.language.iso en_US en_US
dc.publisher Kansas State University en
dc.subject Parameter estimation en_US
dc.subject Black-Scholes-Merton model en_US
dc.title Parameter estimation of the Black-Scholes-Merton model en_US
dc.type Report en_US
dc.description.degree Master of Science en_US
dc.description.level Masters en_US
dc.description.department Department of Statistics en_US
dc.description.advisor James Neill en_US
dc.subject.umi Statistics (0463) en_US
dc.date.published 2013 en_US
dc.date.graduationmonth May en_US


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