XFGIBT03 (MatLab R2007b)

Outputs a plot of state price density estimations, from Derman and Kani IBT, Barle and Cakici IBT, and Monte-Carlo simulation. Require Eulerscheme.m, XFGIBTcdk.m, IBTsdisplot.m, XFGIBTcbc.m, regxest.m, and optionprice.m

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Jun Zheng

Applied Quantitative Finance

kernel, nw

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Fri, July 27 2012 by Dedy Dwi Prastyo

Eulerscheme, XFGIBTcdk, IBTsdisplot, XFGIBTcbc, regxest

XFGIBT03.asv


Description: -


clear all
close all
clc
  %%%simdata = load('C:DokumentyStatistikXFGDataxfgibtmcsimulation20.txt');
  %simd = load('C:ProgrammeMDTechXploRedataxfgXFGIBTmcsimulation20.dat');
  %global simdata;  
  r=0.03			%interest rate
  S=100				%current stock price
  lev=40			%the number of time steps
  expiration=5			%time to expiration(year)
simdata = zeros(lev,1000); 
for j=1:1000
     simdata(:,j) = Eulerscheme(lev,(expiration/lev),r,S);
end
simdata = reshape(simdata',(lev*1000),1);
global simdata 
  [St,AD,p]=XFGIBTcdk(S,r,expiration,lev);
  datdk=[St(:,end) (AD(:,end)*exp(r*expiration))];
  in = find(datdk(:,2)>0.0005);
  %datdk=datdk(in,:);
  bandwidth=20;
  mhdk=IBTsdisplot(datdk, bandwidth);
  [St2,AD2,p2]=XFGIBTcbc(S,r,expiration,lev);
  datbc=[St2(:,end) (AD2(:,end)*exp(r*expiration))];
  in2 = find(datbc(:,2)>0.0005);
  %datbc=datbc(in2,:);
  bandwidth=20;
  mhbc=IBTsdisplot(datbc, bandwidth);
  %slast=simdata(1+49000:50000,:)
slast=simdata(1+19000:20000,:);
qua = @(u) 15/16.*((1-u.^2).^2).*(abs(u)<=1);
  [n,m] = size(slast);
  mx= min(slast);
  rx= max(slast)-min(slast);
  h = 20;
  cK=5/7;           % just for quartic kernel
  c2=1.5;           % just for quartic kernel
  alpha = 0.05;
  s = (slast-mx)./rx;
  h = h./rx;
  [fh2, xi2] = ksdensity(s, 'width', h, 'kernel', qua);
  rr = sqrt(-2*log(h));
  dn = rr + 0.5*log( c2/(2*(pi^2)) )/rr;
  calpha = -log(-log(1-alpha)/2);
  mrg = (calpha/rr + dn) .* sqrt(cK.*fh2/(n*h));
  xi2 = (rx.*xi2 + mx);
  clo = ((fh2 - mrg)/rx);
  cup = ((fh2 + mrg)/rx);
  fh2  = (fh2/rx);
plot(mhdk(:,1),mhdk(:,2),'-.b','LineWidth',3);
hold on
plot(mhbc(:,1),mhbc(:,2),'--k','LineWidth',3);
plot(xi2,fh2,'-r','LineWidth',3);
plot(xi2,clo,':r','LineWidth',2);
plot(xi2,cup, ':r','LineWidth',2);
title('Estimated State Price Density');
xlabel('Stock Price');
ylabel('Probability');
set(gca,'YTick',0:0.005:0.1);
set(gca,'YLim',[0 0.03]);
set(gca,'XLim',[40 180]);
hold off