function xxx = lect03ivsurfparam
clear;
format compact;
pts = load('c:/VolSurf0.dat');
K = pts(:,1);
F = pts(:,2);
C = pts(:,3);
T = pts(:,4)/252;
IV = pts(:,5);
r = 0.03;
VM = mean(IV)
% fit volatility surface
MN = mness(K, F, T);
pars = [ VM, -5., 3., 0.];
opts = optimset('Display','iter','TolFun',0.00001);
x = lsqnonlin(@iverrors,pars,[], [], opts, MN, T, IV);
figure(1);
plot3(MN,T,IV,'o'); hold on;
[DM,TM] = meshgrid(-.2:.02:.6,0:.02:1.2);
ZM = ivfitted(x, DM, TM);
mesh(DM, TM, ZM); hold off;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function y = ivfitted(pars, MN, T)
% The parametrized fitted surface
y = pars(1) + pars(4) * T + pars(3) * exp( pars(2) * T) .* MN;

function y = iverrors(pars, MN, T, IV)
% The parametrization errors
y = ivfitted(pars, MN, T) - IV;

function y = mness(K, F, T)
% The moneyness function
y = log(F./K) ./ sqrt(T);