Abstract
The quasi-Monte Carlo method for financial valuation and other integration problems has error bounds of size O((log N)k N-1), or even O((log N)k N-3/2), which suggests significantly better performance than the error size O(N-1/2) for standard Monte Carlo. But in high-dimensional problems, this benefit might not appear at feasible sample sizes. Substantial improvements from quasi-Monte Carlo integration have, however, been reported for problems such as the valuation of mortgage-backed securities, in dimensions as high as 360. The authors believe that this is due to a lower effective dimension of the integrand in those cases. This paper defines the effective dimension and shows in examples how the effective dimension may be reduced by using a Brownian bridge representation.
Keywords
Monte Carlo methodValuation (finance)Dimension (graph theory)Brownian bridgeQuasi-Monte Carlo methodBrownian motionComputer scienceMathematical optimizationMathematicsEconometricsHybrid Monte CarloActuarial scienceFinanceEconomicsStatisticsMarkov chain Monte CarloCombinatorics
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Publication Info
- Year
- 1997
- Type
- article
- Volume
- 1
- Issue
- 1
- Pages
- 27-46
- Citations
- 511
- Access
- Closed
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Cite This
Russel E. Caflisch,
William J. Morokoff,
Art B. Owen
(1997).
Valuation of mortgage-backed securities using Brownian bridges to reduce effective dimension.
The Journal of Computational Finance
, 1
(1)
, 27-46.
https://doi.org/10.21314/jcf.1997.005
Identifiers
- DOI
- 10.21314/jcf.1997.005