[Quantlib-dev] Basis functions for Longstaff-Schwartz method

[Kakhkhor A. <kab...@gm...>]

Dear All,
Class LsmBasisSystem (lsmbasissystem.hpp) doesn't look good. Its
implementation uses very inefficient and probability broken method to
generate multidimensional basis functions from single factor basis
functions. It generates many duplicates and then uses "remove-o-zap"
method to remove them. The size of basis is not the same for different
polynomial types.  You can see the test results below. I reworked the
implementation, so that basis sizes are the same for all polynomial
types and no duplicates are created during the process. I would like
to submit my code to QuantLib, but not sure how to do it.

Regards,
Kakhkhor Abdijalilov.


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The number of functions returned by multiPathBasisSystem method.

In (n-m), n - size after "remove-o-zap",
m - number of functions removed by "remove-o-zap"

dimension = 1
order; Mnm; Lgr; Hrm; Hpr; Lgn; Chb; Chb2
=========================================
0; 1-0; 1-0; 1-0; 1-0; 1-0; 1-0; 1-0
1; 2-0; 1-1; 2-0; 2-0; 2-0; 2-0; 2-0
2; 3-1; 3-1; 4-0; 3-1; 4-0; 4-0; 4-0
3; 4-4; 5-3; 6-2; 4-4; 7-1; 6-2; 7-1
4; 5-11; 10-6; 10-6; 7-9; 12-4; 10-6; 12-4

dimension = 2
order; Mnm; Lgr; Hrm; Hpr; Lgn; Chb; Chb2
=========================================
0; 1-0; 1-0; 1-0; 1-0; 1-0; 1-0; 1-0
1; 3-0; 1-2; 3-0; 3-0; 3-0; 3-0; 3-0
2; 6-3; 6-3; 8-1; 6-3; 8-1; 8-1; 8-1
3; 10-17; 12-15; 16-11; 10-17; 18-9; 17-10; 18-9
4; 15-66; 32-49; 32-49; 20-61; 38-43; 35-46; 38-43

dimension = 3
order; Mnm; Lgr; Hrm; Hpr; Lgn; Chb; Chb2
=========================================
0; 1-0; 1-0; 1-0; 1-0; 1-0; 1-0; 1-0
1; 4-0; 1-3; 4-0; 4-0; 4-0; 4-0; 4-0
2; 10-6; 10-6; 13-3; 10-6; 13-3; 13-3; 13-3
3; 20-44; 22-42; 32-32; 20-44; 35-29; 34-30; 35-29
4; 35-221; 73-183; 74-182; 44-212; 86-170; 82-174; 86-170

dimension = 4
order; Mnm; Lgr; Hrm; Hpr; Lgn; Chb; Chb2
=========================================
0; 1-0; 1-0; 1-0; 1-0; 1-0; 1-0; 1-0
1; 5-0; 1-4; 5-0; 5-0; 5-0; 5-0; 5-0
2; 15-10; 15-10; 19-6; 15-10; 19-6; 19-6; 19-6
3; 35-90; 35-90; 55-70; 35-90; 59-66; 57-68; 59-66
4; 70-555; 140-485; 144-481; 84-541; 164-461; 154-471; 164-461
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