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Numerical solutions for American opt...

Li, Jinliang.

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Numerical solutions for American options on assets with stochastic volatilities.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Numerical solutions for American options on assets with stochastic volatilities./
Author:	Li, Jinliang.
Description:	69 p.
Notes:	Director: You-lan Zhu.
Contained By:	Dissertation Abstracts International62-12B.
Subject:	Economics, Finance. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3035272
ISBN:	0493479597

Numerical solutions for American options on assets with stochastic volatilities.
Li, Jinliang.

Numerical solutions for American options on assets with stochastic volatilities. - 69 p.

Director: You-lan Zhu.

Thesis (Ph.D.)--The University of North Carolina at Charlotte, 2002.

This thesis discusses American options on assets with stochastic volatilities. First, it gives a proof of the solution uniqueness of the 2-D PDE to evaluate options for both general two-factor model and the model used in this thesis. Second, it formulates the two factor American option as a 2-D PDE free boundary problem. Third, because the solution of this 2-D PDE free boundary problem is not a very smooth function and the free boundary changes rapidly near maturity, most of the numerical methods could fail to find a reasonable solution or the numerical solution has a large truncation error. Instead of solving this 2-D PDE directly, the difference between the solution of the original 2-D PDE free boundary problem and the solution of a 1-D parabolic equation with the same final condition is calculated. The difference function is very smooth in the entire region. We can solve this new 2-D PDE free boundary problem more accurately and more efficiently. Fourth, this paper uses a coordinate transformation to map the moving boundary to a fixed boundary and applies the Singularity Separating Method (SSM) technique to separate the free boundary and find the exact location of the free boundary (the optimal exercise price). This will be very useful for arbitrage activities. Fifth, it develops numerical methods to solve the new free boundary problem and focuses on the high order implicit finite difference method. It provides several methods to solve the nonlinear system. Sixth, It discovers the put-call symmetry relation between American options in the two factor stochastic volatility model. Seventh, it uses the extrapolation technique to improve the approximation accuracy of the numerical solution. Chapter 5 gives several numerical examples.

ISBN: 0493479597Subjects--Topical Terms:

626650
Economics, Finance.

Numerical solutions for American options on assets with stochastic volatilities.
LDR:02658nam 2200277 a 45 001 926690
005 20110422
008 110422s2002 eng d
020 $a 0493479597
035 $a (UnM)AAI3035272
035 $a AAI3035272
040 $a UnM $c UnM
100 1 $a Li, Jinliang. $3 1250274
245 1 0 $a Numerical solutions for American options on assets with stochastic volatilities.
300 $a 69 p.
500 $a Director: You-lan Zhu.
500 $a Source: Dissertation Abstracts International, Volume: 62-12, Section: B, page: 5757.
502 $a Thesis (Ph.D.)--The University of North Carolina at Charlotte, 2002.
520 $a This thesis discusses American options on assets with stochastic volatilities. First, it gives a proof of the solution uniqueness of the 2-D PDE to evaluate options for both general two-factor model and the model used in this thesis. Second, it formulates the two factor American option as a 2-D PDE free boundary problem. Third, because the solution of this 2-D PDE free boundary problem is not a very smooth function and the free boundary changes rapidly near maturity, most of the numerical methods could fail to find a reasonable solution or the numerical solution has a large truncation error. Instead of solving this 2-D PDE directly, the difference between the solution of the original 2-D PDE free boundary problem and the solution of a 1-D parabolic equation with the same final condition is calculated. The difference function is very smooth in the entire region. We can solve this new 2-D PDE free boundary problem more accurately and more efficiently. Fourth, this paper uses a coordinate transformation to map the moving boundary to a fixed boundary and applies the Singularity Separating Method (SSM) technique to separate the free boundary and find the exact location of the free boundary (the optimal exercise price). This will be very useful for arbitrage activities. Fifth, it develops numerical methods to solve the new free boundary problem and focuses on the high order implicit finite difference method. It provides several methods to solve the nonlinear system. Sixth, It discovers the put-call symmetry relation between American options in the two factor stochastic volatility model. Seventh, it uses the extrapolation technique to improve the approximation accuracy of the numerical solution. Chapter 5 gives several numerical examples.
590 $a School code: 0694.
650 4 $a Economics, Finance. $3 626650
650 4 $a Mathematics. $3 515831
690 $a 0405
690 $a 0508
710 2 0 $a The University of North Carolina at Charlotte. $3 1026752
773 0 $t Dissertation Abstracts International $g 62-12B.
790 $a 0694
790 1 0 $a Zhu, You-lan, $e advisor
791 $a Ph.D.
792 $a 2002
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3035272