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Stable Up-Downwind Finite Difference...

Sun, Chong.

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Stable Up-Downwind Finite Difference Methods for Solving Heston Stochastic Volatility Equations.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Stable Up-Downwind Finite Difference Methods for Solving Heston Stochastic Volatility Equations./
Author:	Sun, Chong.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2019,
Description:	117 p.
Notes:	Source: Dissertations Abstracts International, Volume: 81-04, Section: B.
Contained By:	Dissertations Abstracts International81-04B.
Subject:	Finance. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=22583536
ISBN:	9781088336267

Stable Up-Downwind Finite Difference Methods for Solving Heston Stochastic Volatility Equations.
Sun, Chong.

Stable Up-Downwind Finite Difference Methods for Solving Heston Stochastic Volatility Equations. - Ann Arbor : ProQuest Dissertations & Theses, 2019 - 117 p.

Source: Dissertations Abstracts International, Volume: 81-04, Section: B.

Thesis (Ph.D.)--Baylor University, 2019.

This item must not be sold to any third party vendors.

This dissertation explores effective and efficient computational methodologies for solving two-dimensional Heston stochastic volatility option pricing models with multiple financial engineering applications. Dynamically balanced up-downwind finite difference methods taking care of cross financial derivative terms in the partial differential equations involved are implemented and rigorously analyzed. Semi-discretization strategies are utilized over variable data grids for highly vibrant financial market simulations. Moving mesh adaptations are incorporated with experimental validations. The up-downwind finite difference schemes derived are proven to be numerically stable with first-order accuracy in approximations. Discussions on concepts of stability and convergence are fulfilled. Simulation experiments are carefully designed and carried out to illustrate and validate our conclusions. Multiple convergence and relative error estimates are obtained via computations with real data. The novel new methods developed are highly satisfactory with distinguished simplicity and straightforwardness in programming realizations for options markets, especially when unsteady stocks' markets are significant concerns. The research also reveals promising directions for continuing accomplishments in financial mathematics and computations.

ISBN: 9781088336267Subjects--Topical Terms:

542899
Finance.

Stable Up-Downwind Finite Difference Methods for Solving Heston Stochastic Volatility Equations.
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245 1 0 $a Stable Up-Downwind Finite Difference Methods for Solving Heston Stochastic Volatility Equations.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2019
300 $a 117 p.
500 $a Source: Dissertations Abstracts International, Volume: 81-04, Section: B.
500 $a Advisor: Sheng, Qin.
502 $a Thesis (Ph.D.)--Baylor University, 2019.
506 $a This item must not be sold to any third party vendors.
520 $a This dissertation explores effective and efficient computational methodologies for solving two-dimensional Heston stochastic volatility option pricing models with multiple financial engineering applications. Dynamically balanced up-downwind finite difference methods taking care of cross financial derivative terms in the partial differential equations involved are implemented and rigorously analyzed. Semi-discretization strategies are utilized over variable data grids for highly vibrant financial market simulations. Moving mesh adaptations are incorporated with experimental validations. The up-downwind finite difference schemes derived are proven to be numerically stable with first-order accuracy in approximations. Discussions on concepts of stability and convergence are fulfilled. Simulation experiments are carefully designed and carried out to illustrate and validate our conclusions. Multiple convergence and relative error estimates are obtained via computations with real data. The novel new methods developed are highly satisfactory with distinguished simplicity and straightforwardness in programming realizations for options markets, especially when unsteady stocks' markets are significant concerns. The research also reveals promising directions for continuing accomplishments in financial mathematics and computations.
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856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=22583536