/usr/share/octave/packages/financial-0.5.0/blstheta.m is in octave-financial 0.5.0-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 | ## Copyright (C) 2013 Parsiad Azimzadeh <parsiad.azimzadeh@gmail.com>
##
## This program is free software; you can redistribute it and/or modify it under
## the terms of the GNU Lesser General Public License as published by the Free
## Software Foundation; either version 3 of the License, or (at your option) any
## later version.
##
## This program is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
## FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License
## for more details.
##
## You should have received a copy of the GNU Lesser General Public License
## along with this program; if not, see <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {[@var{CallTheta}, @var{PutTheta}] =} blstheta (@var{Price}, @var{Strike}, @var{Rate}, @var{Time}, @var{Volatility})
## @deftypefnx {Function File} {[@var{CallTheta}, @var{PutTheta}] =} blstheta (@var{Price}, @var{Strike}, @var{Rate}, @var{Time}, @var{Volatility}, @var{Yield})
## Compute the Black-Scholes theta.
##
## @itemize @minus{}@minus{}
## @item
## Variable: @var{Price} The current price of the underlying asset.
## @item
## Variable: @var{Strike} The strike price the option is written on.
## @item
## Variable: @var{Rate} The risk-free interest rate.
## @item
## Variable: @var{Time} The time-to-expiry.
## @item
## Variable: @var{Volatility} The volatility of the underlying asset.
## @item
## Variable: @var{Yield} (Optional, default = 0) Annualized, continuously
## compounded rate of dividends of the underlying asset.
## @end itemize
##
## Computes the Black-Scholes theta, the rate of change of the option value with
## respect to the time-to-expiry.
##
## @seealso{blsdelta, blsgamma, blslambda, blsprice, blsrho, blsvega}
## @end deftypefn
function [CallTheta, PutTheta] = blstheta (Price, Strike, Rate, Time, ...
Volatility, Yield = 0)
if (nargin < 5 || nargin > 6)
print_usage ();
endif
blscheck ("blstheta", Price, Strike, Rate, Time, Volatility, Yield);
sqrtT = sqrt (Time);
sigma_sqrtT = Volatility .* sqrtT;
d1 = 1 ./ sigma_sqrtT .* (log (Price ./ Strike) + (Rate - Yield + Volatility.^2 / 2) .* Time);
d2 = d1 - sigma_sqrtT;
phi1 = normcdf (d1);
phi2 = normcdf (d2);
disc = exp (-Yield .* Time);
shift = -disc .* Price .* normpdf (d1) .* Volatility / 2 ./ sqrtT;
t1 = Rate .* Strike .* exp (-Rate .* Time);
t2 = Yield .* Price .* disc;
CallTheta = shift - t1 .* phi2 + t2 .* phi1 ;
PutTheta = shift + t1 .* (1 - phi2) + t2 .* (phi1 - 1);
endfunction
## Tests
%!test
%! [CallTheta, PutTheta] = blstheta (90:10:110, 100, 0.04, 1, 0.2, 0.01);
%! assert (CallTheta, [-4.2901 -5.2337 -5.1954], 1e-4)
%! assert (PutTheta, [-1.3380 -2.3806 -2.4413], 1e-4)
## Test input validation
%!error blstheta ()
%!error blstheta (1)
%!error blstheta (1, 2)
%!error blstheta (1, 2, 3)
%!error blstheta (1, 2, 3, 4)
|