BLACK_SCHOLES
Simple Approaches to the Black-Scholes Equation

BLACK_SCHOLES is a FORTRAN90 library which demonstrates several approaches to the valuation of a European call, creating graphics files for processing by gnuplot, by Desmond Higham.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

BLACK_SCHOLES is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

COLORED_NOISE, a FORTRAN90 library which generates samples of noise obeying a 1/f^alpha power law.

GNUPLOT, FORTRAN90 programs which illustrate how a program can write data and command files so that gnuplot can create plots of the program results.

ORNSTEIN_UHLENBECK, a FORTRAN90 library which approximates solutions of the Ornstein-Uhlenbeck stochastic differential equation (SDE) using the Euler method and the Euler-Maruyama method.

PCE_LEGENDRE, a MATLAB program which assembles the system matrix associated with a polynomal chaos expansion of a 2D stochastic PDE, using Legendre polynomials;

PCE_ODE_HERMITE, a FORTRAN90 program which sets up a simple scalar ODE for exponential decay with an uncertain decay rate, using a polynomial chaos expansion in terms of Hermite polynomials.

PINK_NOISE, a FORTRAN90 library which computes a "pink noise" signal obeying a 1/f power law.

SDE, a FORTRAN90 library which illustrates the properties of stochastic differential equations, and common algorithms for their analysis, by Desmond Higham;

STOCHASTIC_DIFFUSION, a FORTRAN90 library which implements several versions of a stochastic diffusivity coefficient.

STOCHASTIC_GRADIENT_ND_NOISE, a MATLAB program which solves an optimization problem involving a functional over a system with stochastic noise.

STOCHASTIC_RK, a FORTRAN90 library which applies a Runge-Kutta scheme to a stochastic differential equation.

Author:

Original MATLAB version by Desmond Higham;
FORTRAN90 version by John Burkardt.

Reference:

1. Desmond Higham,
   Black-Scholes for Scientific Computing Students,
   Computing in Science and Engineering,
   Volume 6, Number 6, November/December 2004, pages 72-79.

Source Code:

• black_scholes.f90, the source code.

Examples and Tests:

• black_scholes_test.f90, a sample calling program.
• black_scholes_test.txt, the output file.
• asset_path_data.txt, the graphics data file.
• asset_path_commands.txt, the graphics data file.
• asset_path.png, a PNG image of the asset path, created by GNUPLOT.

List of Routines:

• ASSET_PATH simulates the behavior of an asset price over time.
• BINOMIAL uses the binomial method for a European call.
• BSF evaluates the Black-Scholes formula for a European call.
• FORWARD uses the forward difference method to value a European call option.
• GET_UNIT returns a free FORTRAN unit number.
• MC uses Monte Carlo valuation on a European call.
• R8_NORMAL_01 returns a unit pseudonormal R8.
• R8_UNIFORM_01 returns a unit pseudorandom R8.
• R8VEC_NORMAL_01 returns a unit pseudonormal R8VEC.
• R8VEC_PRINT_PART prints "part" of an R8VEC.
• R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN90 source codes.