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asiancontinuous.m

 % Copyright (c) 2008 the authors listed at the following URL, and/or
 % the authors of referenced articles or incorporated external code:
 % http://en.literateprograms.org/Asian_Option_Pricing_(MATLAB)?action=history&offset=20061105065258
 % 
 % Permission is hereby granted, free of charge, to any person obtaining
 % a copy of this software and associated documentation files (the
 % "Software"), to deal in the Software without restriction, including
 % without limitation the rights to use, copy, modify, merge, publish,
 % distribute, sublicense, and/or sell copies of the Software, and to
 % permit persons to whom the Software is furnished to do so, subject to
 % the following conditions:
 % 
 % The above copyright notice and this permission notice shall be
 % included in all copies or substantial portions of the Software.
 % 
 % THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
 % EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
 % MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
 % IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
 % CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
 % TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
 % SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
 % 
 % Retrieved from: http://en.literateprograms.org/Asian_Option_Pricing_(MATLAB)?oldid=7915
 
 function [price, pde_sol] = asiancontinuous(S0,K,r,vol,T)
 % ASIANCONTINUOUS - implementation of Vecer's PDE Method for Asion Option

 % Pricing, minor modifications by Charles-Albert Lehalle.

 % use:

 % [price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)

 % pde_sol.plot()

 
 %Implementation of Vecer's PDE Method

 %Vecer, J. (2002): "Unified Asian Pricing",  Risk, Vol. 15, No. 6, 113-116 

 
 N = 200;       %number of subintervals in space 

 M = 200;       %number of subintervals in time

 
 %more points -> higher precision, but slower

 
 %Xmesh  x

 xmin = -1;
 xmax = 1;
 x = linspace(xmin, xmax, N+1);
 
 %Tspan

 t = linspace(0, T, M+1);
 
 
 m = 0;
 sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
 pde_sol = struct('x', x, 't', t, 'u', sol(:,:,1), 'plot', @plot_sol);
 
 
 %Output of the value of the option

 X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
 x0 = X_0/S0;
 
 uout = pdeval(m,x,sol(M+1,:),x0);
 price = uout*S0;
 
 
 fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

 
 function [c, f, s] = pdef(x, t, u, DuDx)
 c = 1;
 
     f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
     s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;
 
 end
 
 
 function u0 = pdeic(x)
 u0 = max(x, 0);
 end
 
 
 function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
 pl = ul;
 ql = 0;
 pr = ur - xr;
 qr = 0;
 end
 
 
 function h = plot_sol
 figure('Color',[0.9412 0.9412 0.9412 ]);
 surf(pde_sol.x, pde_sol.t, pde_sol.u, 'edgecolor', 'none');
 axis([min(pde_sol.x) max(pde_sol.x) min(pde_sol.t) max(pde_sol.t) min(min(pde_sol.u)) max(max(pde_sol.u))]);
 xlabel('X');ylabel('t');
 end
 
 
 end
 

test_asiancontinuous.m

 % Copyright (c) 2008 the authors listed at the following URL, and/or
 % the authors of referenced articles or incorporated external code:
 % http://en.literateprograms.org/Asian_Option_Pricing_(MATLAB)?action=history&offset=20061105065258
 % 
 % Permission is hereby granted, free of charge, to any person obtaining
 % a copy of this software and associated documentation files (the
 % "Software"), to deal in the Software without restriction, including
 % without limitation the rights to use, copy, modify, merge, publish,
 % distribute, sublicense, and/or sell copies of the Software, and to
 % permit persons to whom the Software is furnished to do so, subject to
 % the following conditions:
 % 
 % The above copyright notice and this permission notice shall be
 % included in all copies or substantial portions of the Software.
 % 
 % THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
 % EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
 % MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
 % IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
 % CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
 % TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
 % SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
 % 
 % Retrieved from: http://en.literateprograms.org/Asian_Option_Pricing_(MATLAB)?oldid=7915
 
 [price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
 pde_sol.plot()