How does functions and lsqnonlin work?

Question

Martin 2012-6-6

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/40422-how-does-functions-and-lsqnonlin-work

I have created a code to calibrate option data to a mean-reverting model. It looks like this: _______________________________________________________________________

clear all

load('callopt.mat');

% K=strike, T=time to expiration in year fraction % Market=market option prices

K=callopt(:,3); T=callopt(:,2); market=callopt(:,10); r=0.01;

x0=(2 2 2 2);

[x,resnorm]=lsqnonlin(@(theta) myfun(theta,K,T,r,market),x02); ___________________________________________________________________

function F=myfun(theta,K,T,r,market)

bet=theta(1); rev=theta(2); V=theta(3); sig=theta(4);

vega=4*rev*bet/(sig^2);

gam=(4*bet)/((sig^2)*(1-exp(-bet*T)));

lambda=vega*exp(-bet*T)*V;

model=exp(-r.*T).*(exp(-bet.*T).*V.*ncx2cdf(gam.*K,vega+4,lambda))+rev.*(1-exp(-bet.*T)).*ncx2cdf(gam.*K,vega+2,lambda)-K.*ncx2cdf(gam.*K,vega,lambda);

F=(market-model);

___________________________________________________________________

The starting guess for my parameters are in x0. My problem is that no matter which number i input as the fourth number (that is the initial guess for sig), then when lsqnonlin is done the answer for sig is always the same as the initial guess. I have a feeling that maybe its because vega and gam is not recalculated for every iteration of lsqnonlin, seeing that sig only appears in vega and gam.

Can someone elaborate how the steps for lsqnonlin are, so that I can understand the process better?