# Calibrating VIX option data to model - lsqnonlin problem

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Martin on 4 Jun 2012
Im new to MatLab and in the process of learning it. Currently im trying to calibrate VIX option market data to Mean-reverting volatility process. To begin with im just trying to get an output without errors.
I have coded this script and the following function: ___________________________________________________________________________ clear all
global K; global T; global r; global market;
%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(@myfun,x0); ___________________________________________________________________________
function F=myfun(bet,rev,V,sig)
global K; global T; global r; global market;
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); ___________________________________________________________________________
This is the complete error i receive: Error using myfun (line 5) Not enough input arguments.
Error in lsqnonlin (line 197) initVals.F = feval(funfcn{3},xCurrent,varargin{:});
Error in meanrev (line 15) [x,resnorm]=lsqnonlin(@myfun,x0); Caused by: Failure in initial user-supplied objective function evaluation. LSQNONLIN cannot continue.
Can someone help?

Richard Crozier on 4 Jun 2012
lsqnonlin does not know that myfun takes 4 arguments, it expects it to just take one. You can get around this using an 'anonymous' function call like so:
[x,resnorm]=lsqnonlin(@(argthatchanges) myfun(argthatchanges,rev,V,sig), x0);
Note that I don't know which of your argument your actually solving for, so you may need to change about. Read about anonymous functions to understand better how this works.
Incidentally it is good programming practice to avoid the use of global variables unless absolutely necessary.

Martin on 4 Jun 2012
Thank you very much! I think this will solve my problem. I will try and implement it later tonight.
Martin on 4 Jun 2012
I tried the first thing you suggested and that worked great.
Then i tried to implement the anonymous function, but i couldnt get that to work.
My codes now looks like this:
________________________________________________
clear all
%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=[1,1,1,1];
[x,resnorm]=lsqnonlin(@(theta)myfun(theta,K,T,r,market,x0));
____________________________________________________
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);
___________________________________________________________________
Error using lsqnonlin (line 161)
The input to LSQNONLIN should be either a structure with
valid fields or consist of at least two arguments.
Error in meanrev (line 15)
[x,resnorm]=lsqnonlin(@(theta)myfun(theta,K,T,r,market,x0));
______________________________________________________
Did i miss something?
Another question I have is, if it is possible to weight each of the numbers in the vector F differently? It is market practice to weight each market price by its bid-ask spread.
The loss function to minimized will then look like this: L(theta) = sum(w_i(Market - Model(theta))^2)
where w_i is each individual weight.
I thought of just expanding F to be F=w_i(market-model), but this would be unfortunate as I understand lsqnonlin minimize the square of F and I dont want the weights to be squared as well. If you know what i mean?
Martin on 5 Jun 2012
To the question regarding weights i guess i could just take sqrt(w_i)*(Market-Model) and then when running the lsqnonlin it would look as i want it?