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Near expiry asymptotics of implied v...

Ma, Shihan.

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Near expiry asymptotics of implied volatility in local volatility models.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Near expiry asymptotics of implied volatility in local volatility models./
Author:	Ma, Shihan.
Description:	59 p.
Notes:	Source: Dissertation Abstracts International, Volume: 71-05, Section: B, page: 3127.
Contained By:	Dissertation Abstracts International71-05B.
Subject:	Applied Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3402216
ISBN:	9781109742138

Near expiry asymptotics of implied volatility in local volatility models.
Ma, Shihan.

Near expiry asymptotics of implied volatility in local volatility models. - 59 p.

Source: Dissertation Abstracts International, Volume: 71-05, Section: B, page: 3127.

Thesis (Ph.D.)--Northwestern University, 2010.

In this thesis we firstly express a direct link between local and implied volatilities in the form of a quasilinear degenerate parabolic partial differential equation, following Berestycki, Busca and Florent's work in [1]. Then, we derive the asymptotic form of pricing formula with constant coefficients. Next, we introduce the parametrix method. Using the parametrix method leads us to the lower and upper bounds of the fundamental solution of the parabolic partial differential solution with variable coefficients. Using the expansion of the transition probability of 1-dimensional Brownian Motion with drift, and applying Girsanov's theorem, we could get the leading term in the fundamental solution. Finally, we give the asymptotic formula of the implied volatility near expiry.

ISBN: 9781109742138Subjects--Topical Terms:

1669109
Applied Mathematics.

Near expiry asymptotics of implied volatility in local volatility models.
LDR:01763nam 2200301 4500 001 1391281
005 20110110132613.5
008 130515s2010 ||||||||||||||||| ||eng d
020 $a 9781109742138
035 $a (UMI)AAI3402216
035 $a AAI3402216
040 $a UMI $c UMI
100 1 $a Ma, Shihan. $3 1669686
245 1 0 $a Near expiry asymptotics of implied volatility in local volatility models.
300 $a 59 p.
500 $a Source: Dissertation Abstracts International, Volume: 71-05, Section: B, page: 3127.
500 $a Adviser: Elton P. Hsu.
502 $a Thesis (Ph.D.)--Northwestern University, 2010.
520 $a In this thesis we firstly express a direct link between local and implied volatilities in the form of a quasilinear degenerate parabolic partial differential equation, following Berestycki, Busca and Florent's work in [1]. Then, we derive the asymptotic form of pricing formula with constant coefficients. Next, we introduce the parametrix method. Using the parametrix method leads us to the lower and upper bounds of the fundamental solution of the parabolic partial differential solution with variable coefficients. Using the expansion of the transition probability of 1-dimensional Brownian Motion with drift, and applying Girsanov's theorem, we could get the leading term in the fundamental solution. Finally, we give the asymptotic formula of the implied volatility near expiry.
590 $a School code: 0163.
650 4 $a Applied Mathematics. $3 1669109
650 4 $a Economics, Finance. $3 626650
690 $a 0364
690 $a 0508
710 2 $a Northwestern University. $b Mathematics. $3 1280008
773 0 $t Dissertation Abstracts International $g 71-05B.
790 1 0 $a Hsu, Elton P., $e advisor
790 1 0 $a Pinsky, Mark A. $e committee member
790 1 0 $a Zabell, Sandy L. $e committee member
790 $a 0163
791 $a Ph.D.
792 $a 2010
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3402216