American Options

Emperiments with different libraries and (eventually) algorithms for pricing American Options. Currently only using a standard binomial model.

The various implementation in AmrPut* is based on the R-code from Rolf Poulsen's FAMØS paper Amerikanske optioner og finansielle beregninger.

Compiling Haskell Versions

The Haskell implementations do not define a Main module, so in order to compile them to standalone executables you have to pass an appropriate -main-is option to GHC. For example:

ghc -O3 --make AmrPut.hs -main-is AmrPut -o AmrPut

Check the source file for the module name to use.

Benmark Results from Haskell Version(s)

Experiments done using Haskell library criterion, on a MacBook Pro (early-2010 model).

Data.Vector.Unboxed, optimised with GHC 7.4.2 -O3 (AmrPut.hs)

    Fuction call            Time (ms)
    ------------------------------------
    AmrPut.binom 1          0.8 ±   0.02
    AmrPut.binom 16       207   ±   6
    AmrPut.binom 30       941   ±  36
    AmrPut.binom 64      5576   ±  58 
    AmrPut.binom 128    27750   ± 468 

Fusable Functional Vectors in Standard ML

The experiments below demonstrate that the use of fusable functional vectors (FFVs) can give a runtime improvement of more than 20 percent compared to a Vector/VectorSlice implementation. The experiments were done running with Mlton on a MacBook Pro (mid-2012 model):

Vector/VectorSlice (AmrPut.sml):

     bash-3.2$ time ./AmrPutVec 
     AmrPut.binom(1) = 6.74543295136
     AmrPut.binom(8) = 13.9456888384
     AmrPut.binom(16) = 16.2225913859
     AmrPut.binom(30) = 17.6537059071
     AmrPut.binom(64) = 18.4299315651
     AmrPut.binom(128) = 18.5737326153

     real    0m17.551s
     user    0m17.499s
     sys     0m0.046s

Functional Vectors (AmrPutVec.sml):

     bash-3.2$ time ./AmrPutVec 
     AmrPut.binom(1) = 6.74543295136
     AmrPut.binom(8) = 13.9456888384
     AmrPut.binom(16) = 16.2225913859
     AmrPut.binom(30) = 17.6537059071
     AmrPut.binom(64) = 18.4299315651
     AmrPut.binom(128) = 18.5737326153

     real    0m13.288s
     user    0m13.272s
     sys     0m0.015s

With the use of Unsafe.Vector in the implementation of the Fvec.memoize function, real time drops to 12.57s.

To redo the experiments, for each case, alter the file AmrPutVecTest.sml appropriately and run

$ make AmrPutVec; time ./AmrPutVec

To get the desired speedups, the programmer is required to insert memoize operations at subtle places in the source code; see the file AmrPutVec.sml for details.