IBTcrr (MatLab R2007b)
computes European option prices using a binomial tree for assets with no/continuous dividends assuming a constant implied volatility. Required by XFGIBT01.m and XFGIBT02.m.
Click the button to demonstrate a graph view.
Notice: This content requires Java Runtime Environment.
Java Applet and JavaScript should be allowed on your browser.
Fri, July 27 2012 by Dedy Dwi Prastyo
C = IBTcrr(S0, K, r, sig, T, n, flag)
- Price of underlying asset, Strike price, Interest rate, Implied Volatility, Time to expiration, Number of steps in the tree, Flag for Call/Put option
- Price of an European option.
Description: C = IBTcrr(100, 80, 0.03, 0.1, 1, 4, 1) option flag (1 for call, 0 for put)
function [price]=IBTcrr(s0, k, i, sig, t, n, flag) type=1; % 0 is American/1 is European div=0; if s0<=0 disp('IBTcrr: Price of Underlying Asset should be positive! Please input again') s0=input('s0='); end if k<0 disp('IBTcrr: Exercise price couldnot be negative! Please input again') k=input('k='); end if sig<0 disp('IBTcrr: Volatility should be positive! Please input again') sig=input('sig='); end if t<=0 disp('IBTcrr: Time to expiration should be positive! Please input again') t=input('t='); end if n<1 disp('IBTcrr: Number of steps should be at least equal to 1! Please input again') n=input('n='); end if (n>150) % Constraint of n, otherwise it will take too much time disp('IBTcrr: Could you please choose a smaller n? Please input again') n=input('n='); end dt=t/n; % Interval of step u=exp(sig.*sqrt(dt)); % Up movement parameter u d=1./u; % Down movement parameter d b=i-div; % Costs of carry p=0.5+0.5*(b-sig^2/2)*sqrt(dt)/sig; % Probability of up movement s=ones(n+1,n+1)*s0; un=ones(n+1,1)-1; un(n+1,1)=1; dm=un'; um=[]; j=1; while j<n+1 d1=[ones(1,n-j)-1 (ones(1,j+1)*d).^((1:j+1)-1)]; dm=[dm; d1]; % Down movement dynamics u1=[ones(1,n-j)-1 (ones(1,j+1)*u).^((j:-1:0))]; um=[um; u1]; % Up movement dynamics j=j+1; end um=[un';um]'; dm=dm'; s=s(1,1).*um.*dm; % Stock price development Stock_Price=s; s=flipud(s); % Rearangement opt = zeros(size(s)); if flag == 1 & type==0 % Option is a american call opt(:,n+1) = max(s(:,n+1)-k,0); % Determine option values from prices for j = n:-1:1; l = 1:j; discopt = ((1-p)*opt(l,j+1)+p*opt(l+1,j+1))*exp(-b*dt); opt(:,j) = [max(s(1:j,j)-k,discopt);zeros(n+1-j,1)]; end American_Call_Price = flipud(opt); elseif flag == 1 & type==1 % Option is a european call opt(:,n+1) = max(s(:,n+1)-k,0); % Determine option values from prices for j = n:-1:1; l = 1:j; discopt = ((1-p)*opt(l,j+1)+p*opt(l+1,j+1))*exp(-b*dt); opt(:,j) = [discopt;zeros(n+1-j,1)]; end European_Call_Price = flipud(opt); %disp(' ') ; %disp('The price of the option at time t_0 is') price=European_Call_Price(n+1,1); elseif flag == 0 & type==0 % Option is an american put opt(:,n+1) = max(k-s(:,n+1),0); % Determine option values from prices for j = n:-1:1 l = 1:j; discopt = ((1-p)*opt(l,j+1)+p*opt(l+1,j+1))*exp(-b*dt); opt(:,j) = [max(k-s(1:j,j),discopt);zeros(n+1-j,1)]; end American_Put_Price = flipud(opt); elseif flag == 0 & type==1 % Option is a european put opt(:,n+1) = max(k-s(:,n+1),0); % Determine option values from prices for j = n:-1:1 l = 1:j; discopt = ((1-p)*opt(l,j+1)+p*opt(l+1,j+1))*exp(-b*dt); opt(:,j) = [discopt;zeros(n+1-j,1)]; end European_Put_Price = flipud(opt); %disp(' ') ; %disp('The price of the option at time t_0 is') price=European_Put_Price(n+1,1); end