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Options pricing - application of ray...

Hu, Fannu.

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Options pricing - application of ray methods and singular perturbations.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Options pricing - application of ray methods and singular perturbations./
Author:	Hu, Fannu.
Description:	124 p.
Notes:	Source: Dissertation Abstracts International, Volume: 71-12, Section: B, page: .
Contained By:	Dissertation Abstracts International71-12B.
Subject:	Applied Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3431240
ISBN:	9781124304854

Options pricing - application of ray methods and singular perturbations.
Hu, Fannu.

Options pricing - application of ray methods and singular perturbations. - 124 p.

Source: Dissertation Abstracts International, Volume: 71-12, Section: B, page: .

Thesis (Ph.D.)--University of Illinois at Chicago, 2010.

Option pricing is an active area in financial industry. The development of option pricing problems has resulted in the employment of many mathematical techniques. I apply the ray method of geometrical optics and matched asymptotic expansions to some option pricing models. This includes the constant elasticity of variance (CEV) process and the Black-Scholes (BS) model.

ISBN: 9781124304854Subjects--Topical Terms:

1669109
Applied Mathematics.

Options pricing - application of ray methods and singular perturbations.
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008 130515s2010 ||||||||||||||||| ||eng d
020 $a 9781124304854
035 $a (UMI)AAI3431240
035 $a AAI3431240
040 $a UMI $c UMI
100 1 $a Hu, Fannu. $3 1673069
245 1 0 $a Options pricing - application of ray methods and singular perturbations.
300 $a 124 p.
500 $a Source: Dissertation Abstracts International, Volume: 71-12, Section: B, page: .
500 $a Adviser: Charles Knessl.
502 $a Thesis (Ph.D.)--University of Illinois at Chicago, 2010.
520 $a Option pricing is an active area in financial industry. The development of option pricing problems has resulted in the employment of many mathematical techniques. I apply the ray method of geometrical optics and matched asymptotic expansions to some option pricing models. This includes the constant elasticity of variance (CEV) process and the Black-Scholes (BS) model.
520 $a We consider the CEV model with knock-out barriers, in the limit of small volatility. We show that the asymptotic structure of the CEV model can lead to caustics, caustic boundaries and interesting "corner" and "transition" layers, where the solutions are expressed in terms of Airy functions.
520 $a We also examine American up-and-out put barrier options and American floating strike lookback put options under the BS model, which correspond to moving boundary problems for partial differential equations (PDEs). We consider the PDEs in the limit of a low interest rate and/or large volatility. This limit is particularly relevant to today's financial crisis. We show the importance of separately analyzing the different space-time scales.
590 $a School code: 0799.
650 4 $a Applied Mathematics. $3 1669109
650 4 $a Economics, Finance. $3 626650
690 $a 0364
690 $a 0508
710 2 $a University of Illinois at Chicago. $3 1020478
773 0 $t Dissertation Abstracts International $g 71-12B.
790 1 0 $a Knessl, Charles, $e advisor
790 $a 0799
791 $a Ph.D.
792 $a 2010
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3431240