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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.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Near expiry asymptotics of implied volatility in local volatility models./
作者:	Ma, Shihan.
面頁冊數:	59 p.
附註:	Source: Dissertation Abstracts International, Volume: 71-05, Section: B, page: 3127.
Contained By:	Dissertation Abstracts International71-05B.
標題:	Applied Mathematics. -
電子資源:	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.
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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
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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