section 1. Calculating sensitivity of the price of derivatives American or European option using binomial tree model

section 2. Calculating first order greeks

the code compiles till this point value = optionM(1,1); unable to proceed to the next iteration to calculate the delta, gamma,vega, rho Kindly give your inputs

Thanks in Advance

function [value,delta,gamma,theta,vega,rho] = BinomialTreeGreeks(putCall,...
% This function calculates the American or European option value by a
% binomal tree model.
% [value,delta,gamma,theta,vega,rho] = ...
% BinomialTreeGreeks(putCall,exerciseType,S0,K,sigma,r,div,T,n)
% Input: putCall: indicates the option type
% putCall = ’Call’ for a call option
% putCall = ’Put’ for a put
% option
% exerciseType: European (’E’) or American (’A’)
% exercise type
% S: Stock price
% K: Strike price
% sigma: Volatility
% r: riskfree rate
% div: Dividend yield
% T: Time to maturity
% n: Number of steps in the tree
% OUTPUT: value: option value
% delta: dV/dS
% gamma: dV^2/d^2S
% theta: dV/dT
% vega: dV/dsigma
% rho: dV/dr
% EXAMPLE: [value,delta,gamma,theta,vega,rho] = ...
% BinomialTreeGreeks(’Put’,’A’,50,50,0.4,0.05,0.02,2,500)
% Parameters for binomial tree
dt = T/n;
u = exp(sigma*sqrt(dt));
d = 1/u;
p = (exp((r-div)*dt)-d)/(u-d);
q = 1-p;
disc = exp(-r*dt);
% Initialize matrices
stockM = zeros(n+1,n+1);
optionM = zeros(n+1,n+1);
% Create stock tree
stockM (1,1) = S0;
for j = 2:n+1
for i = 1:j-1
stockM(i,j) = stockM(i,j-1)*u;
stockM(i+1,j) = stockM(i,j-1)*d;
% Set z parameter to calculate the option payoff depending on the
% selected option type (Call, Put)
switch putCall
case 'Call'
z = 1;
case 'Put'
z = -1;
error('Check option type!');
% Insert terminal values
optionM(:,end) = max(z*(stockM(:,end)-K),0);
% Value call by working backward from time n-1 to time 0
switch exerciseType
% European option
case 'E'
for j=n:-1:1;
for i=j:-1:1;
optionM(i,j) = disc*(p*optionM(i,j+1)+q*optionM(i+1,j+1));
% American exercise type
case 'A'
for j=n:-1:1;
for i=j:-1:1;
optionM(i,j) = max(z*(stockM(i,j)-K),disc*(p*optionM(i,j+1)+q*optionM(i+1,j+1)));
error('Check exercise type!');
value = optionM(1,1);
% Calculate greeks
if nargout > 1
delta = (optionM(1,2)-optionM(2,2))/(stockM(1,2)-stockM(2,2));
if nargout > 2
deltaUp = (optionM(1,3)-optionM(2,3))/(stockM(1,3)-stockM(2,3));
deltaDown = (optionM(2,3)-optionM(3,3))/(stockM(2,3)-stockM(3,3));
gamma = (deltaUp-deltaDown)/((stockM(1,3)-stockM(3,3))/2);
if nargout > 3
theta = (optionM(2,3)-optionM(1,1))/(2*dt);
% Calculate vega and rho with re-evaluation
if nargout > 4
vegaUp = feval(@BinomialTreeGreeks,putCall,exerciseType,S0,K,...
vegaDown = feval(@BinomialTreeGreeks,putCall,exerciseType,S0,K,...
vega = (vegaUp - vegaDown)/(2*0.01);
if nargout > 5
rhoUp = feval(@BinomialTreeGreeks,putCall,exerciseType,S0,K,sigma,...
rhoDown = feval(@BinomialTreeGreeks,putCall,exerciseType,S0,K,sigma,...
rho = (rhoUp - rhoDown)/(2*0.01);

closed as off-topic by Bob Jansen Jun 16 '15 at 11:21

  • This question does not appear to be about quantitative finance within the scope defined in the help center.
If this question can be reworded to fit the rules in the help center, please edit the question.

  • 2
    $\begingroup$ I'm voting to close this question as off-topic because it's unclear how the code is used and the code is hard to read due to a lack of indentation. $\endgroup$ – Bob Jansen Jun 16 '15 at 11:21
  • $\begingroup$ sorry @BobJansen, i'm new to this space, i should have known to put the code properly, $\endgroup$ – Matlab_Quant Jun 17 '15 at 19:44
  • $\begingroup$ code uses standard Binomial implementation and calculates the price of the option and thereafter uses a combination of finite difference methods to compute the value of greeks given by their respective formulas $\endgroup$ – Matlab_Quant Jun 17 '15 at 19:45
  • $\begingroup$ You can edit all the necessary information into your question, even when it's closed. As it stands it's still not really clear what you're asking and what is going wrong. $\endgroup$ – Bob Jansen Jun 17 '15 at 20:17
  • $\begingroup$ Please consider to edit it and give at least brief description of what you're trying to do. What kind of problems that you have. What you don't understand etc. Once you've done it, people including myself might spend some time to read your code. $\endgroup$ – SmallChess Jun 18 '15 at 1:49

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