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Quasi-Monte Carlo methods in finance.

Jiang, Xuefeng.

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Quasi-Monte Carlo methods in finance.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Quasi-Monte Carlo methods in finance./
Author:	Jiang, Xuefeng.
Description:	104 p.
Notes:	Adviser: John R. Birge.
Contained By:	Dissertation Abstracts International68-03B.
Subject:	Economics, Finance. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3258536

Quasi-Monte Carlo methods in finance.
Jiang, Xuefeng.

Quasi-Monte Carlo methods in finance. - 104 p.

Adviser: John R. Birge.

Thesis (Ph.D.)--Northwestern University, 2007.

The classic error bounds for quasi-Monte Carlo approximation follow the Koksma-Hlawka inequality based on the assumption that the integrand has finite variation. Unfortunately, not all functions have this property. In particular, integrands for common applications in finance, such as option pricing, do not typically have bounded variation. In contrast to this lack of theoretical precision, quasi-Monte Carlo methods perform quite well empirically. This research provides some theoretical justification for these observations. We present new error bounds for a broad class of option pricing problems using quasi-Monte Carlo approximation in one and multiple dimensions. The method for proving these error bounds uses a recent result of Niederreiter (2003) and does not require bounded variation or other smoothness properties.Subjects--Topical Terms:

626650
Economics, Finance.

Quasi-Monte Carlo methods in finance.
LDR:02439nam 2200289 a 45 001 963750
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035 $a (UMI)AAI3258536
035 $a AAI3258536
040 $a UMI $c UMI
100 1 $a Jiang, Xuefeng. $3 1286813
245 1 0 $a Quasi-Monte Carlo methods in finance.
300 $a 104 p.
500 $a Adviser: John R. Birge.
500 $a Source: Dissertation Abstracts International, Volume: 68-03, Section: B, page: 1863.
502 $a Thesis (Ph.D.)--Northwestern University, 2007.
520 $a The classic error bounds for quasi-Monte Carlo approximation follow the Koksma-Hlawka inequality based on the assumption that the integrand has finite variation. Unfortunately, not all functions have this property. In particular, integrands for common applications in finance, such as option pricing, do not typically have bounded variation. In contrast to this lack of theoretical precision, quasi-Monte Carlo methods perform quite well empirically. This research provides some theoretical justification for these observations. We present new error bounds for a broad class of option pricing problems using quasi-Monte Carlo approximation in one and multiple dimensions. The method for proving these error bounds uses a recent result of Niederreiter (2003) and does not require bounded variation or other smoothness properties.
520 $a This research also provides numerical experiments on application of quasi-Monte Carlo methods. We apply quasi-Monte Carlo sequences in a duality approach to value American options. We compare the results and computational effort using different low discrepancy sequences. The results demonstrate the value of sequences using expansions of irrationals.
520 $a We then apply quasi-Monte Carlo simulation to LIBOR market models based on the Brace-Gatarek-Musiela/Jamshidian framework. We price an exotic interest-rate derivative, in particular, a European payer swaption and compare the results using pseudo random sequences and different low discrepancy sequences. We also tested randomized quasi-Monte Carlo methods and apply importance sampling to quasi-Monte Carlo simulation.
590 $a School code: 0163.
650 4 $a Economics, Finance. $3 626650
650 4 $a Engineering, Industrial. $3 626639
690 $a 0508
690 $a 0546
710 2 0 $a Northwestern University. $3 1018161
773 0 $t Dissertation Abstracts International $g 68-03B.
790 $a 0163
790 1 0 $a Birge, John R., $e advisor
791 $a Ph.D.
792 $a 2007
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3258536