# Black-Scholes option pricing benchmark **URL:** \ **Category:** Uncategorized\ **Created:** [October 16, 2021, 9:00pm UTC](https://fortran-lang.discourse.group/t/black-scholes-option-pricing-benchmark/2097 "2021-10-16T21:00:07Z")\ **Posts on this page:** 12\ **Page:** 1
**Author:** ![Beliavsky](https://avatars.discourse-cdn.com/v4/letter/b/ba8739/32.png) [@Beliavsky](https://fortran-lang.discourse.group/u/Beliavsky)\ **Post date:** [October 16, 2021, 9:00pm UTC](https://fortran-lang.discourse.group/t/black-scholes-option-pricing-benchmark/2097/1 "2021-10-16T21:00:07Z")
The [Black-Scholes option pricing formula](https://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model) in Fortran is ```auto pure elemental function call_price(s,k,r,t,vol) result(price) ! Black-Scholes price of a European call option real(kind=dp), intent(in) :: s ! stock price real(kind=dp), intent(in) :: k ! strike price real(kind=dp), intent(in) :: r ! annual interest rate -- 0.02 means 2% real(kind=dp), intent(in) :: t ! time to expiration in years real(kind=dp), intent(in) :: vol ! annualized volatility -- 0.30 means 30% real(kind=dp) :: price ! call price real(kind=dp) :: d1,d2,vol_sqrt_t vol_sqrt_t = vol*sqrt(t) d1 = (log(s/k) + (r + 0.5_dp*vol**2)*t)/vol_sqrt_t d2 = d1 - vol_sqrt_t price = s*cumnorm(d1) - k*exp(-r*t)*cumnorm(d2) end function call_price ``` Calling the function 10^8 times took 10.2 and 3.4 seconds on Windows 10 using gfortran and Intel Fortran (specifically gfortran 12.0.0 20210718 from [equation.com](http://equation.com) and Intel Fortran Version 2021.1 Build 20201112\_000000), both using the -O3 option. The full code is [here](https://github.com/Beliavsky/Black-Scholes). Suggested speedups are welcome. A trading firm may make markets in hundreds of thousands of options and must recalculate the option prices when the underlying stock prices move, so quickly calculating option prices and sensitivities (partial derivatives of option price wrt stock price, volatility etc.) is important to it. ---
**Author:** ![fortran4r](https://avatars.discourse-cdn.com/v4/letter/f/9de0a6/32.png) [@fortran4r](https://fortran-lang.discourse.group/u/fortran4r)\ **Post date:** [October 16, 2021, 9:08pm UTC](https://fortran-lang.discourse.group/t/black-scholes-option-pricing-benchmark/2097/2 "2021-10-16T21:08:39Z")
I also have my BSM function in Fortran. I use the erf function to construct cumnorm. Not sure about the performance difference. But using the erf function makes my code much more concise. ---
**Author:** ![vmagnin](https://yyz2.discourse-cdn.com/free1/user_avatar/fortran-lang.discourse.group/vmagnin/32/28_2.png) [@vmagnin](https://fortran-lang.discourse.group/u/vmagnin)\ **Post date:** [October 17, 2021, 10:40am UTC](https://fortran-lang.discourse.group/t/black-scholes-option-pricing-benchmark/2097/3 "2021-10-17T10:40:09Z")
> [@Beliavsky](#): > > Calling the function 10^8 times took 10.2 and 3.4 seconds on Windows 10 using gfortran and Intel Fortran (specifically gfortran 12.0.0 20210718 from [equation.com](http://equation.com) and Intel Fortran Version 2021.1 Build 20201112\_000000), both using the -O3 option. No big difference between GFortran and ifort under Ubuntu 21.04 (Intel(R) Core™ i3-3220 CPU @ 3.30GHz): ```bash $ ifort -O3 -stand:f18 kind.f90 black_scholes.f90 xxblack_scholes.f90 && ./a.out c = 4.75942232590152 time elapsed = 6.57875600000000 $ gfortran-11 -O3 -std=f2018 kind.f90 black_scholes.f90 xxblack_scholes.f90 && ./a.out c = 4.7594223259015216 time elapsed = 6.4030679999999993 $ gfortran-11 --version GNU Fortran (Ubuntu 11.1.0-1ubuntu1~21.04) 11.1 [...] $ ifort --version ifort (IFORT) 2021.4.0 20210910 ``` ---
**Author:** ![certik](https://yyz2.discourse-cdn.com/free1/user_avatar/fortran-lang.discourse.group/certik/32/4_2.png) [@certik](https://fortran-lang.discourse.group/u/certik)\ **Post date:** [October 17, 2021, 2:19pm UTC](https://fortran-lang.discourse.group/t/black-scholes-option-pricing-benchmark/2097/4 "2021-10-17T14:19:10Z")
Nice. On Apple M1 I am getting 1.8s with both GFortran 11.0.1: ```auto + gfortran -O3 -march=native -ffast-math -funroll-loops -c kind.f90 -o kind.o + gfortran -O3 -march=native -ffast-math -funroll-loops -c black_scholes.f90 -o black_scholes.o + gfortran -O3 -march=native -ffast-math -funroll-loops -c xxblack_scholes.f90 -o xxblack_scholes.o + gfortran -O3 -march=native -ffast-math -funroll-loops -o xxblack_scholes xxblack_scholes.o black_scholes.o kind.o + ./xxblack_scholes c = 4.7594223259015269 real 0m1.853s user 0m1.846s sys 0m0.004s ``` and the latest LFortran master: ```auto + lfortran --fast -c kind.f90 -o kind.o + lfortran --fast -c black_scholes.f90 -o black_scholes.o + lfortran --fast -c xxblack_scholes.f90 -o xxblack_scholes.o + lfortran --fast -o xxblack_scholes xxblack_scholes.o black_scholes.o kind.o + ./xxblack_scholes c = 4.75942232590152159 real 0m1.808s user 0m1.801s sys 0m0.004s ``` I had to apply a tiny patch as we still have to implement the `cpu_time` and also as a workaround for [LLVM: Calling f(g(x)) in a loop can run out of stack (#573) · Issues · lfortran / lfortran · GitLab](https://gitlab.com/lfortran/lfortran/-/issues/573) (which I really need to fix soon): ```diff diff --git a/xxblack_scholes.f90 b/xxblack_scholes.f90 index 27dc187..45866a3 100644 --- a/xxblack_scholes.f90 +++ b/xxblack_scholes.f90 @@ -8,13 +8,15 @@ implicit none integer, parameter :: niter = 10**8 integer :: iter real(kind=dp) :: c,t1,t2 -call cpu_time(t1) +real(dp) s,k,r,t,vol +!call cpu_time(t1) ! Example 15.6 p360 of Options, Futures, and other Derivatives (2015), 9th edition, ! by John C. Hull +s=42;k=40;r=0.1_dp;t=0.5_dp;vol=0.2_dp do iter=1,niter - c = call_price(s=42.0_dp,k=40.0_dp,r=0.1_dp,t=0.5_dp,vol=0.2_dp) ! Hull gets 4.76 + c = call_price(s, k, r, t, vol) ! Hull gets 4.76 end do print*,"c =",c -call cpu_time(t2) -print*,"time elapsed = ",t2-t1 +!call cpu_time(t2) +!print*,"time elapsed = ",t2-t1 end program xxblack_scholes ``` The patch is really minimal, I am very happy about that! It gives the same answer as GFortran. I am also happy about the performance. Credit goes to LLVM, we don’t do any optimizations ourselves yet, but we will in the coming months. LLVM compiles code slowly (compared to what is possible, but LFortran compiles this in 0.224s compared to GFortran 0.342s, both with optimizations on), but the performance of the final executable is excellent. They have done an A+ job. So did GFortran, because they have implemented all this from scratch, and on this benchmark it’s essentially equivalent. Update: I implemented `cpu_time()` in [!1491](https://gitlab.com/lfortran/lfortran/-/merge_requests/1491) and [!1492](https://gitlab.com/lfortran/lfortran/-/merge_requests/1492), so now the diff is just: ```diff diff --git a/xxblack_scholes.f90 b/xxblack_scholes.f90 index 27dc187..e5df36c 100644 --- a/xxblack_scholes.f90 +++ b/xxblack_scholes.f90 @@ -8,11 +8,13 @@ implicit none integer, parameter :: niter = 10**8 integer :: iter real(kind=dp) :: c,t1,t2 +real(dp) s,k,r,t,vol call cpu_time(t1) ! Example 15.6 p360 of Options, Futures, and other Derivatives (2015), 9th edition, ! by John C. Hull +s=42;k=40;r=0.1_dp;t=0.5_dp;vol=0.2_dp do iter=1,niter - c = call_price(s=42.0_dp,k=40.0_dp,r=0.1_dp,t=0.5_dp,vol=0.2_dp) ! Hull gets 4.76 + c = call_price(s, k, r, t, vol) ! Hull gets 4.76 end do print*,"c =",c call cpu_time(t2) ``` ---
**Author:** ![certik](https://yyz2.discourse-cdn.com/free1/user_avatar/fortran-lang.discourse.group/certik/32/4_2.png) [@certik](https://fortran-lang.discourse.group/u/certik)\ **Post date:** [October 20, 2021, 12:41am UTC](https://fortran-lang.discourse.group/t/black-scholes-option-pricing-benchmark/2097/5 "2021-10-20T00:41:20Z")
And with fixing keyword arguments ([!1498](https://gitlab.com/lfortran/lfortran/-/merge_requests/1498)) and an alloca bug ([!1494](https://gitlab.com/lfortran/lfortran/-/merge_requests/1494)), this benchmark now works without any modifications! ```auto $ lfortran --fast -c kind.f90 -o kind.o $ lfortran --fast -c black_scholes.f90 -o black_scholes.o $ lfortran --fast -c xxblack_scholes.f90 -o xxblack_scholes.o $ lfortran --fast -o xxblack_scholes xxblack_scholes.o black_scholes.o kind.o $ ./xxblack_scholes c = 4.75942232590152159 time elapsed = 1.83060800000000001 ``` @Beliavsky give it a shot. You have to use the latest master of LFortran. ---
**Author:** ![Beliavsky](https://avatars.discourse-cdn.com/v4/letter/b/ba8739/32.png) [@Beliavsky](https://fortran-lang.discourse.group/u/Beliavsky)\ **Post date:** [October 20, 2021, 1:58am UTC](https://fortran-lang.discourse.group/t/black-scholes-option-pricing-benchmark/2097/6 "2021-10-20T01:58:07Z")
> [@certik](#): > > @Beliavsky give it a shot. You have to use the latest master of LFortran. Thanks for the update. Before on WSL2 I followed the [instructions](https://lfortran.org/blog/2021/09/lfortran-minimum-viable-product-mvp/) ```auto git clone https://gitlab.com/lfortran/examples/mvp_demo.git cd mvp_demo conda create -n mvp_demo -c conda-forge fpm=0.4.0 lfortran=0.14.0 conda activate mvp_demo fpm run --all --compiler=lfortran fpm test --compiler=lfortran ``` to install. What .git should I clone to get the master? I tried `https://gitlab.com/lfortran/lfortran.git` , but when I do that I still cannot compile `cpu_time()`. `lfortran --version` says ```auto LFortran version: 0.14.0 Platform: Linux Default target: x86_64-unknown-linux-gnu ``` ---
**Author:** ![certik](https://yyz2.discourse-cdn.com/free1/user_avatar/fortran-lang.discourse.group/certik/32/4_2.png) [@certik](https://fortran-lang.discourse.group/u/certik)\ **Post date:** [October 20, 2021, 2:39am UTC](https://fortran-lang.discourse.group/t/black-scholes-option-pricing-benchmark/2097/7 "2021-10-20T02:39:20Z")
You can download the Development version from: [Download - LFortran](https://lfortran.org/download/) and follow the instructions from [Installation - LFortran Documentation](https://docs.lfortran.org/installation/#build-from-a-source-tarball). So: ```auto conda create -n lf python cmake llvmdev=11.1.0 conda activate lf wget https://lfortran.github.io/tarballs/dev/lfortran-0.14.0-678-g95c94e7e.tar.gz tar xzf lfortran-0.14.0-678-g95c94e7e.tar.gz cd lfortran-0.14.0-678-g95c94e7e cmake -DWITH_LLVM=yes -DCMAKE_INSTALL_PREFIX=`pwd`/inst . make -j8 make install ``` This will install the `lfortran` into the `inst/bin`, in the current directory. I just tested it and it works. The only difference to the online instructions is to pin the `llvmdev=11.1.0` dependency, as we don’t compile yet with a newer LLVM versions. ---
**Author:** ![Beliavsky](https://avatars.discourse-cdn.com/v4/letter/b/ba8739/32.png) [@Beliavsky](https://fortran-lang.discourse.group/u/Beliavsky)\ **Post date:** [October 20, 2021, 4:05am UTC](https://fortran-lang.discourse.group/t/black-scholes-option-pricing-benchmark/2097/8 "2021-10-20T04:05:58Z")
Thanks, that works. I get run times of 3.95 and 3.02 s for LFortran and gfortran. The script used is ```auto exec=a.out FC="../lfortran --fast" FC="gfortran -O3" # comment out to use lfortran rm -f *.o $exec $FC -c kind.f90 $FC -c black_scholes.f90 $FC -c xxblack_scholes.f90 $FC -o $exec xxblack_scholes.o black_scholes.o kind.o ./$exec ``` I am surprised that gfortran is much faster here on WSL2 than plain Windows, on which the program takes 10s. Another program compiled with gfortran takes 1.0 and 0.67s on Windows and WSL2. I wonder if programs compiled with gfortran are generally faster on WSL2 than Windows. ---
**Author:** ![CRquantum](https://yyz2.discourse-cdn.com/free1/user_avatar/fortran-lang.discourse.group/crquantum/32/730_2.png) [@CRquantum](https://fortran-lang.discourse.group/u/CRquantum)\ **Post date:** [October 20, 2021, 6:31am UTC](https://fortran-lang.discourse.group/t/black-scholes-option-pricing-benchmark/2097/9 "2021-10-20T06:31:18Z")
For some code, in my experience, gfortran on plain windows can be slower than gfortran on linux by a factor of 6 or so. I do not know why, perhaps somehow gfortran did not take full advantage of windows SDK when generating and linking the exe file? However, the speed of gfortran on WSL2 should be basically the same as on linux, after all WSL is basically linux. ---
**Author:** ![certik](https://yyz2.discourse-cdn.com/free1/user_avatar/fortran-lang.discourse.group/certik/32/4_2.png) [@certik](https://fortran-lang.discourse.group/u/certik)\ **Post date:** [October 20, 2021, 11:45am UTC](https://fortran-lang.discourse.group/t/black-scholes-option-pricing-benchmark/2097/10 "2021-10-20T11:45:10Z")
Perfect, thanks for trying it out! So on your computer you get LFortran 3.95s, Intel 3.4s, GFortran 3.02s? Very cool. ---
**Author:** ![Beliavsky](https://avatars.discourse-cdn.com/v4/letter/b/ba8739/32.png) [@Beliavsky](https://fortran-lang.discourse.group/u/Beliavsky)\ **Post date:** [October 20, 2021, 3:33pm UTC](https://fortran-lang.discourse.group/t/black-scholes-option-pricing-benchmark/2097/11 "2021-10-20T15:33:30Z")
Using all compilers on WSL 2, I get lfortran 3.99 s gfortran 3.05 s ifort 3.27 s flang 3.38 s The script used is ```auto #!/bin/bash exec=a.out declare compilers=("../lfortran --fast" "gfortran -O3" "ifort -O3" "flang -O3") declare sources=(kind.f90 black_scholes.f90 xxblack_scholes.f90) declare objs=(kind.o black_scholes.o xxblack_scholes.o) for FC in "${compilers[@]}"; do # loop over compilers echo && echo $FC $FC --version rm -f *.o $exec # cleanup for src in "${sources[@]}"; do $FC -c $src done $FC -o $exec "${objs[@]}" ./$exec done ``` giving output ```auto ../lfortran --fast LFortran version: 0.14.0-678-g95c94e7e Platform: Linux Default target: x86_64-unknown-linux-gnu c = 4.75942232590152159 time elapsed = 3.98533099999999996 gfortran -O3 GNU Fortran (Ubuntu 9.3.0-17ubuntu1~20.04) 9.3.0 Copyright (C) 2019 Free Software Foundation, Inc. This is free software; see the source for copying conditions. There is NO warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. c = 4.7594223259015216 time elapsed = 3.0451200000000003 ifort -O3 ifort (IFORT) 2021.2.0 20210228 Copyright (C) 1985-2021 Intel Corporation. All rights reserved. c = 4.75942232590152 time elapsed = 3.26698100000000 flang -O3 clang version 7.0.1 Target: x86_64-pc-linux-gnu Thread model: posix InstalledDir: /usr/bin c = 4.759422325901522 time elapsed = 3.376587867736816 ``` Are there other compilers to try on WSL 2? Bash question – what is the recommended way to set `objs`, given `sources`. I just copied and pasted and replaced `.f90` with `.o`. ---
**Author:** ![certik](https://yyz2.discourse-cdn.com/free1/user_avatar/fortran-lang.discourse.group/certik/32/4_2.png) [@certik](https://fortran-lang.discourse.group/u/certik)\ **Post date:** [October 20, 2021, 4:23pm UTC](https://fortran-lang.discourse.group/t/black-scholes-option-pricing-benchmark/2097/12 "2021-10-20T16:23:47Z")
Very cool. Would you mind please posting the benchmark to [GitHub - fortran-lang/benchmarks: Fortran benchmarks](https://github.com/fortran-lang/benchmarks) ? Just create a directory for it and put in the source code + build scripts. Let’s start collecting such benchmarks and we’ll eventually create some nice infrastructure to run them with various compilers and options. Can you please also try `gfortran -O3 -march=native -ffast-math -funroll-loops`? Those are the options I typically use. I didn’t see any difference on this particular benchmark, but I see differences on other benchmarks.