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Analysis of nonlinear Black Scholes models

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Please use this identifier to cite or link to this item: http://hdl.handle.net/1928/11130

Analysis of nonlinear Black Scholes models

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dc.contributor.author Qiu, Yan
dc.date.accessioned 2010-09-09T22:09:30Z
dc.date.available 2010-09-09T22:09:30Z
dc.date.issued 2010-09-09
dc.date.submitted July 2010
dc.identifier.uri http://hdl.handle.net/1928/11130
dc.description.abstract The Black Scholes equation is a fundamental model for derivative pricing. Modifying its assumptions will lead to more realistic but mathematically more complicated models. This dissertation consists of analytical and numerical studies about one particular type of nonlinear Black Scholes models, whose nonlinearity lies in the highest spatial derivative 1 with discontinuous coefficient function. First we smooth out the discontinuous term and focus only on the nonlinearity. We consider the case where the volatility is a smooth function and present some basic existence and uniqueness results. To study the discontinuity we simplify the problem by discretizing the Partial Differential Equation PDE only in time and consider the evolution in a given tiny time step from initial data. We perform convergence and perturbation analysis to the Ordinary Differential Equation (ODE) with discontinuous coefficient and obtain some insight of how the curves, where the discontinuity occurs, evolve in the space-time plane for the PDE. Last we obtain numerical results for the nonlinear PDE in the setting of a moving boundary problem. en_US
dc.language.iso en_US en_US
dc.subject Black Scholes Model en_US
dc.subject Nonlinear PDE en_US
dc.subject Moving Boundary Problem en_US
dc.subject.lcsh Derivative securities--Prices--Mathematical models.
dc.subject.lcsh Nonlinear partial differential operators.
dc.title Analysis of nonlinear Black Scholes models en_US
dc.type Dissertation en_US
dc.description.degree Mathematics en_US
dc.description.level Doctoral en_US
dc.description.department University of New Mexico. Dept. of Mathematics and Statistics en_US
dc.description.advisor Lorenz, Jens
dc.description.committee-member Embid, Pedro
dc.description.committee-member Sauer, Christine
dc.description.committee-member Pereyra, Cristina


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