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{CallTheta}, @var{PutTheta}] =} blstheta (@var{Price}, @var{Strike}, @var{Rate}, @var{Time}, @var{Volatility}) 18## @deftypefnx {Function File} {[@var{CallTheta}, @var{PutTheta}] =} blstheta (@var{Price}, @var{Strike}, @var{Rate}, @var{Time}, @var{Volatility}, @var{Yield}) 19## Compute the Black-Scholes theta. 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 Black-Scholes theta, the rate of change of the option value with 38## respect to the time-to-expiry. 39## 40## @seealso{blsdelta, blsgamma, blslambda, blsprice, blsrho, blsvega} 41## @end deftypefn 42 43function [CallTheta, PutTheta] = blstheta (Price, Strike, Rate, Time, ... 44 Volatility, Yield = 0) 45 46 if (nargin < 5 || nargin > 6) 47 print_usage (); 48 endif 49 50 blscheck ("blstheta", Price, Strike, Rate, Time, Volatility, Yield); 51 52 sqrtT = sqrt (Time); 53 sigma_sqrtT = Volatility .* sqrtT; 54 55 d1 = 1 ./ sigma_sqrtT .* (log (Price ./ Strike) + (Rate - Yield + Volatility.^2 / 2) .* Time); 56 d2 = d1 - sigma_sqrtT; 57 58 phi1 = normcdf (d1); 59 phi2 = normcdf (d2); 60 61 disc = exp (-Yield .* Time); 62 shift = -disc .* Price .* normpdf (d1) .* Volatility / 2 ./ sqrtT; 63 t1 = Rate .* Strike .* exp (-Rate .* Time); 64 t2 = Yield .* Price .* disc; 65 66 CallTheta = shift - t1 .* phi2 + t2 .* phi1 ; 67 PutTheta = shift + t1 .* (1 - phi2) + t2 .* (phi1 - 1); 68 69endfunction 70 71## Tests 72%!test 73%! [CallTheta, PutTheta] = blstheta (90:10:110, 100, 0.04, 1, 0.2, 0.01); 74%! assert (CallTheta, [-4.2901 -5.2337 -5.1954], 1e-4) 75%! assert (PutTheta, [-1.3380 -2.3806 -2.4413], 1e-4) 76 77## Test input validation 78%!error blstheta () 79%!error blstheta (1) 80%!error blstheta (1, 2) 81%!error blstheta (1, 2, 3) 82%!error blstheta (1, 2, 3, 4) 83