/usr/share/octave/packages/financial-0.5.0/blsgamma.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.
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##
## 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{Gamma} =} blsgamma (@var{Price}, @var{Strike}, @var{Rate}, @var{Time}, @var{Volatility})
## @deftypefnx {Function File} {@var{Gamma} =} blsgamma (@var{Price}, @var{Strike}, @var{Rate}, @var{Time}, @var{Volatility}, @var{Yield})
## Compute Black-Scholes gamma.
##
## @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 gamma, the rate of change of the option delta with
## respect to the value of the underlying asset.
##
## @seealso{blsdelta, blslambda, blsprice, blsrho, blstheta, blsvega}
## @end deftypefn
function Gamma = blsgamma (Price, Strike, Rate, Time, Volatility, Yield = 0)
if (nargin < 4 || nargin > 5)
print_usage ();
endif
blscheck ("blsgamma", Price, Strike, Rate, Time, Volatility, Yield);
sigma_sqrtT = Volatility .* sqrt (Time);
d1 = 1 ./ sigma_sqrtT .* (log (Price ./ Strike) + (Rate - Yield + ...
Volatility .^2 / 2) .* Time);
Gamma = exp (-Yield .* Time) .* normpdf (d1) ./ (Price .* sigma_sqrtT);
endfunction
## Tests
%assert (blsgamma(90:10:110, 100, 0.04, 1, 0.2, 0.01), [0.0211 0.0191 0.0138], 1e-4)
## Test input validation
%!error blsgamma ()
%!error blsgamma (1)
%!error blsgamma (1, 2)
%!error blsgamma (1, 2, 3)
%!error blsgamma (1, 2, 3, 4)
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