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Sobol Sequences (July, 2014)

Article Summary:

GGY has introduced an option to use the Quasi Monte-Carlo Sobol sequence instead of random numbers when generating real-world or risk-neutral scenarios with HWLN and G2++ and LN models.


The Quasi Monte-Carlo Sobol sequence is a renowned algorithm for generating low discrepancy sequences of points in high-dimensional vector space. Low discrepancy sequences, when used instead of sequences of random numbers, can result in a significant decrease in the Mean Square Error (MSE [1]) of an estimate for the average calculated with the Monte-Carlo method.

In internal testing, the Quasi Monte-Carlo method using Sobol sequences demonstrated MSE reduction in the range from 1 to 10 for different equity derivatives. Derivatives tested included vanilla European options and ratchets (modelling liability guarantees) with various strikes and terms.

Implementation of the Sobol sequence generator in AXIS is based on licensed software created by UK company BRODA Ltd.

If you are interested in learning more about the implementation of Sobol low-discrepancy sequences in AXIS, please contact us through our support portal at www.ggy.com/client.

Note:

[1] The overall error in this case should be measured by the Mean Square Error (MSE). In the case of Monte-Carlo it coincides with the variance of the estimate; in the case of numeric integration, it coincides with the square of the difference between an estimate obtained from the numeric integration method and true value.

 

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