Abstract
In the past decade, quasi-Monte Carlo (QMC) method has become an important numerical tool in computational finance. This is driven, in part, by the sophistication of the models and, in part, by the complexity of the derivative securities. In this paper, we consider an enhanced QMC method recently proposed by Imai and Tan (2009). This method is known as the generalized linear transformation (GLT) and it increases the effciency of QMC via dimension reduction. GLT can be used to simulate general stochastic processes and hence has a much wider range of applications. By assuming that the dynamics of the underlying asset price follows an exponen-tial Meixner Lévyprocessandbyresortingtosome exotic options including average options and lookback options, we demonstrate the effectiveness and robustness of GLT and it substantially outperforms the standard applications of QMC and Monte Carlo methods.
| Original language | English |
|---|---|
| Pages (from-to) | 1-11 |
| Number of pages | 11 |
| Journal | IAENG International Journal of Applied Mathematics |
| Volume | 39 |
| Issue number | 4 |
| Publication status | Published - 2009 Nov |
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Keywords
- Computational finance
- Derivative securities
- Dimension reduction
- Quasi-Monte carlo
ASJC Scopus subject areas
- Applied Mathematics
Cite this
Dimension reduction approach to simulating exotic options in a Meixner Levy market. / Imai, Junichi; Tan, Ken Seng.
In: IAENG International Journal of Applied Mathematics, Vol. 39, No. 4, 11.2009, p. 1-11.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Dimension reduction approach to simulating exotic options in a Meixner Levy market
AU - Imai, Junichi
AU - Tan, Ken Seng
PY - 2009/11
Y1 - 2009/11
N2 - In the past decade, quasi-Monte Carlo (QMC) method has become an important numerical tool in computational finance. This is driven, in part, by the sophistication of the models and, in part, by the complexity of the derivative securities. In this paper, we consider an enhanced QMC method recently proposed by Imai and Tan (2009). This method is known as the generalized linear transformation (GLT) and it increases the effciency of QMC via dimension reduction. GLT can be used to simulate general stochastic processes and hence has a much wider range of applications. By assuming that the dynamics of the underlying asset price follows an exponen-tial Meixner Lévyprocessandbyresortingtosome exotic options including average options and lookback options, we demonstrate the effectiveness and robustness of GLT and it substantially outperforms the standard applications of QMC and Monte Carlo methods.
AB - In the past decade, quasi-Monte Carlo (QMC) method has become an important numerical tool in computational finance. This is driven, in part, by the sophistication of the models and, in part, by the complexity of the derivative securities. In this paper, we consider an enhanced QMC method recently proposed by Imai and Tan (2009). This method is known as the generalized linear transformation (GLT) and it increases the effciency of QMC via dimension reduction. GLT can be used to simulate general stochastic processes and hence has a much wider range of applications. By assuming that the dynamics of the underlying asset price follows an exponen-tial Meixner Lévyprocessandbyresortingtosome exotic options including average options and lookback options, we demonstrate the effectiveness and robustness of GLT and it substantially outperforms the standard applications of QMC and Monte Carlo methods.
KW - Computational finance
KW - Derivative securities
KW - Dimension reduction
KW - Quasi-Monte carlo
UR - http://www.scopus.com/inward/record.url?scp=77955666396&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77955666396&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:77955666396
VL - 39
SP - 1
EP - 11
JO - IAENG International Journal of Applied Mathematics
JF - IAENG International Journal of Applied Mathematics
SN - 1992-9978
IS - 4
ER -