dc.contributor.advisor Pasik-Duncan, Bozenna dc.contributor.author Wang, Peixin dc.date.accessioned 2016-11-10T23:48:54Z dc.date.available 2016-11-10T23:48:54Z dc.date.issued 2016-05-31 dc.date.submitted 2016 dc.identifier.other http://dissertations.umi.com/ku:14453 dc.identifier.uri http://hdl.handle.net/1808/21914 dc.description.abstract The financial world is a world of random things and unpredictable events. Along with the innovative development of diversity and complexity in modern financial market, there are more and more financial derivative emerged in the financial industry in order to gain higher yields as well as hedge the risk . As a result, to price the derivative , indeed the future uncertainty, become an interesting topic in the field of mathematical finance and financial quantitative analysis. In this thesis, I mainly focus on the application of stochastic differential equations to option pricing. Based on the arbitrage-free and risk-neutral assumption, I used the stochastic differential equations theory to solve the pricing problem for the European option of which underlying assets can be described by a geometric Brownian motion. The thesis explores the Black-Scholes model and forms an optimal control problem for the volatility that is an essential parameter in the Black-Scholes formula. Furthermore, the application of backward stochastic differential equations (BSDEs) has been discussed. I figured that BSDEs can model the pricing problem in a more clarifying and logical way. Also, based on the model discussed in the thesis, I provided a case study on pricing a Chinese option-like deposit product by using Mathematica, that shows the feasibility and applicability for the option pricing method based on stochastic differential equations. dc.format.extent 60 pages dc.language.iso en dc.publisher University of Kansas dc.rights Copyright held by the author. dc.subject Mathematics dc.subject Applied mathematics dc.subject Black-Scholes model dc.subject BSDE dc.subject Mathematica dc.subject optimal cotrol dc.subject option pricing dc.subject stochastic differential equation dc.title Application of stochastic differential equations to option pricing dc.type Thesis dc.contributor.cmtemember Hu, Yaozhong dc.contributor.cmtemember Talata, Zsolt dc.thesis.degreeDiscipline Mathematics dc.thesis.degreeLevel M.A. dc.identifier.orcid dc.rights.accessrights openAccess
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