IBTvolaplot (MatLab R2007b)

shows the implied local volatility surface sigma(S,tau) in the implied tree at different time and stock price levels. Required by XFGIBT02.m.

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Jun Zheng

Applied Quantitative Finance

XFGIBT02

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Fri, July 27 2012 by Dedy Dwi Prastyo

IBTvolaplot(loc, step, startpoint, endpoint, m)

- a surface plot to show the implied local volatility


 function[XI,YI,f] = IBT2volaplot(loc, step, startpoint, endpoint, l)
 [v,w] = size(loc);
 if w~= 3
     error('IBT2volaplot: data matrix must contain 3 columns');
 end
 if (step<=0)
     error('IBT2volaplot: the time bandwidth needs to be larger than 0');
 end
 if ((l<0) || (floor(l)~=l))
     error('IBT2volaplot: the number of the steps should be a natural number');
 end
  leng=(endpoint-startpoint)/l;
  while (startpoint<min(loc(:,1))-leng)
  %    disp('IBT2volaplot: startpoint is too small');
  %    disp('Input a new startpoint:');
  %    startpoint = input('startpoint=');
  end
  while (endpoint> max(loc(:,1))+leng)
      disp('IBT2volaplot: endpoint is too large');
      disp('Input a new endpoint:');
      endpoint = input('endpoint=');
  end
  ti = 1:1:l+1;
  [XI,YI] = meshgrid(ti,ti);
  XI = (startpoint-leng)+leng.*XI;
  YI = step.*YI;
  X = reshape(XI,(l+1)^2,1);
  Y = reshape(YI,(l+1)^2,1);
  n=length(X);
  f=zeros(n,1);
  j=1;
  while(j<n+1)
    s=0;
    m1=X(j);
    m2=Y(j);
    k=1;
    while(k< length(loc)+1)
      if(abs(loc(k,1)-X(j)-leng/2)<leng/2 && loc(k,2)==Y(j))
        f(j)=f(j)+loc(k,3);
        f(j);
        s=s+1;
      end
      k=k+1;
    end
    if(s>0) 
      f(j)=f(j)/s;
    end
	j=j+1;
  end
  d = [X Y f];
  XI = XI(1,:)';
  YI = YI(:,1);
  f = reshape(f,l+1,l+1);
  surf(XI,YI,f);
  title('Implied Local Volatility Surface');
  xlabel('Strike Price');
  ylabel('Maturity');