1## Copyright (C) 2013 Parsiad Azimzadeh <parsiad.azimzadeh@gmail.com> 2## 3## This program is free software; you can redistribute it and/or modify it under 4## the terms of the GNU Lesser General Public License as published by the Free 5## Software Foundation; either version 3 of the License, or (at your option) any 6## later version. 7## 8## This program is distributed in the hope that it will be useful, but WITHOUT 9## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or 10## FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License 11## for more details. 12## 13## You should have received a copy of the GNU Lesser General Public License 14## along with this program; if not, see <http://www.gnu.org/licenses/>. 15 16## -*- texinfo -*- 17## @deftypefn {Function File} {[@var{Call}, @var{Put}] =} blsprice (@var{Price}, @var{Strike}, @var{Rate}, @var{Time}, @var{Volatility}) 18## @deftypefnx {Function File} {[@var{Call}, @var{Put}] =} blsprice (@var{Price}, @var{Strike}, @var{Rate}, @var{Time}, @var{Volatility}, @var{Yield}) 19## Compute European call and put option prices. 20## 21## @itemize 22## @item 23## Variable: @var{Price} The current price of the underlying asset. 24## @item 25## Variable: @var{Strike} The strike price the option is written on. 26## @item 27## Variable: @var{Rate} The risk-free interest rate. 28## @item 29## Variable: @var{Time} The time-to-expiry. 30## @item 31## Variable: @var{Volatility} The volatility of the underlying asset. 32## @item 33## Variable: @var{Yield} (Optional, default = 0) Annualized, continuously 34## compounded rate of dividends of the underlying asset. 35## @end itemize 36## 37## Computes the European call and put option prices using the Black-Scholes 38## model. 39## 40## @seealso{blskprice, blsdelta, blsgamma, blsimpv, blslambda, blsrho, blstheta, blsvega} 41## @end deftypefn 42 43function [Call, Put] = blsprice (Price, Strike, Rate, Time, Volatility, ... 44 Yield = 0) 45 46 if (nargin < 5 || nargin > 6) 47 print_usage (); 48 endif 49 50 blscheck ("blsprice", Price, Strike, Rate, Time, Volatility, Yield); 51 52 sigma_sqrtT = Volatility .* sqrt (Time); 53 54 d1 = 1 ./ sigma_sqrtT .* (log (Price ./ Strike) + (Rate - Yield + ... 55 Volatility.^2 / 2) .* Time); 56 d2 = d1 - sigma_sqrtT; 57 58 phi1 = normcdf (d1); 59 phi2 = normcdf (d2); 60 disc = exp (-Rate .* Time); 61 F = Price .* exp ((Rate - Yield) .* Time); 62 63 Call = disc .* (F .* phi1 - Strike .* phi2 ); 64 Put = disc .* (Strike .* (1 - phi2) + F .* (phi1 - 1)); 65 66endfunction 67 68## Tests 69%!test 70%! [Call, Put] = blsprice (90:10:110, 100, 0.04, 1, 0.2, 0.01); 71%! assert (Call, [4.4037 9.3197 16.1217], 1e-4) 72%! assert (Put, [11.3781 6.3937 3.2952], 1e-4) 73 74## Test input validation 75%!error blsprice () 76%!error blsprice (1) 77%!error blsprice (1, 2) 78%!error blsprice (1, 2, 3) 79%!error blsprice (1, 2, 3, 4) 80%!error blsprice ("invalid", "type", "argument", 4, 5) 81%!error blsprice ({1, 2, 3}, [2 7 8], [8 3 1], 4, 10) 82