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{CallEl}, @var{PutEl}] =} blslambda (@var{Price}, @var{Strike}, @var{Rate}, @var{Time}, @var{Volatility})
18## @deftypefnx {Function File} {[@var{CallEl}, @var{PutEl}] =} blslambda (@var{Price}, @var{Strike}, @var{Rate}, @var{Time}, @var{Volatility}, @var{Yield})
19## Computes elasticity of option under the Black-Scholes model.
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 elasticity of an option under the Black-Scholes model.
38## Elasticity measures the percent change in the option price per percent change
39## in the underlying asset price.
40##
41## Update: the following bug has been fixed in MATLAB R2014a(5.3):
42## There is a bug in the MATLAB version of blslambda in which the deltas of the
43## option are not discounted by @var{Yield} in the nonzero dividend case. That
44## is, they compute normcdf(d1) * S / V when they should compute
45## exp(-Yield*T) * normcdf(d1) * S / V. At the time of writing, this bug is
46## present in the financial toolbox shipped with R2013a. Both this version of
47## blslambda and that shipped with R2013a agree when there are no dividends.
48##
49## @seealso{blsdelta, blsgamma, blsprice, blsrho, blstheta, blsvega}
50## @end deftypefn
51
52function [CallEl, PutEl] = blslambda (Price, Strike, Rate, Time, ...
53                                      Volatility, Yield = 0)
54
55  if (nargin < 5 || nargin > 6)
56    print_usage ();
57  endif
58
59  blscheck ("blslambda", Price, Strike, Rate, Time, Volatility, Yield);
60
61  [Call, Put] = blsprice (Price, Strike, Rate, Time, Volatility, Yield);
62  [CallDelta, PutDelta] = blsdelta (Price, Strike, Rate, Time, Volatility, ...
63                                    Yield);
64
65  CallEl = CallDelta .* Price ./ Call;
66  PutEl  = PutDelta  .* Price ./ Put;
67
68endfunction
69
70## Tests
71%!test
72%! [CallEl, PutEl] = blslambda (90:10:110, 100, 0.04, 1, 0.2);
73%! assert (CallEl, [7.7536 6.2258 5.0647], 1e-4)
74%! assert (PutEl, [-4.8955 -6.3639 -7.8941], 1e-4)
75%!test
76%! [CallEl, PutEl] = blslambda (90:10:110, 100, 0.04, 1, 0.2, 0.01);
77%! assert (CallEl, [7.9108 6.3601 5.1762], 1e-4)
78%! assert (PutEl, [-4.7695 -6.2139 -7.7255], 1e-4)
79
80## Test input validation
81%!error blslambda ()
82%!error blslambda (1)
83%!error blslambda (1, 2)
84%!error blslambda (1, 2, 3)
85%!error blslambda (1, 2, 3, 4)
86