Languages: BLACK_SCHOLES is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB 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: 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. black_scholes.sh , BASH commands to compile the source code. Examples and Tests: black_scholes_prb.f90 , a sample calling program. black_scholes_prb.sh , BASH commands to compile and run the sample program. black_scholes_prb_output.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.
asa121 , a library which evaluates the trigamma function, by BE Schneider; this is a version of Applied Statistics Algorithm 121; asa136 , a library which implements a clustering algorithm, by Hartigan and Wong; this is a version of Applied Statistics Algorithm 136; asa144 , a library which randomly generates tables with given row and column sums, by James Boyett; this is a version of Applied Statistics Algorithm 144; asa147 , a library which evaluates the incomplete Gamma function, by Chi Leung Lau; this is a version of Applied Statistics Algorithm 147; asa152 , a library which evaluates the probability density function (PDF) and cumulative density function (CDF) associated with the hypergeometric distribution, by Richard Lund; this is a version of Applied Statistics Algorithm 152; asa159 , a library which computes a random table with given row and column sums, by Michael Patefield; this is a version of Applied Statistics Algorithm 159; asa172 , a library which generates all multidimensional indices in a given range, simulating the behavior of an arbitrary number of nested loops, by OFlaherty and MacKenzie; this is a version of Applied Statistics Algorithm 172; asa183 , a library which implements a random number generator (RNG), by Wichman and Hill; this is a version of Applied Statistics Algorithm 183; asa189 , a library which estimates the parameters of a beta binomial distribution based on a sample of values generated by the distribution, by D Smith; this is a version of Applied Statistics Algorithm 189; asa205 , a library which generates tables with given row and column sums; this is a version of Applied Statistics Algorithm 205; asa226 , a library which evaluates the noncentral incomplete Beta function, by Russell Lenth; this is a version of Applied Statistics Algorithm 226; asa239 , a library which evaluates the incomplete Gamma function, by Shea; this is a version of Applied Statistics Algorithm 239; asa241 , a library which computes the inverse of the normal cumulative density function (CDF), by Michael Wichura; this is a version of Applied Statistics Algorithm 241; asa243 , a library which evaluates the lower tail of the noncentral Student's T distribution, by Russell Lenth; this is a version of Applied Statistics Algorithm 243; asa245 , a library which evaluates the logarithm of the Gamma function, by Allan Mcleod; this is a version of Applied Statistics Algorithm 245; asa266 , a library which evaluates various properties of the Dirichlet probability density function (PDF); this is a version of Applied Statistics Algorithm 266; asa299 , a library which computes the lattice points (integer coordinates) in an M-dimensional simplex, by Chasalow and Brand; this is a version of Applied Statistics Algorithm 299; asa310 , a library which evaluates the noncentral incomplete Beta function, by Chattamvelli and Shanmugam; this is a version of Applied Statistics Algorithm 310; asa314 , a library which computes the inverse of a matrix whose elements are subject to modulo arithmetic, by Roger Payne. This is a version of Applied Statistics Algorithm 314. backtrack_binary_rc , a library which carries out a backtrack search for a set of binary decisions, using reverse communication.
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