add hw code

clf

clear all

s0 = 5;%initial price

n = 10; %% n sample paths 

dur = 1000;

step = 10000;

dt = dur/step;

Vect = linspace(0,dur,step); 

u = 0.10;

sigma = 0.3;

r = randn(n,step);

cr = cumsum(r,2);

increm = u*dt+sigma*sqrt(dt)*r-0.5*sigma^2*dt*r.^2;

logRatio = (ones(n,1)*Vect)*(u - sigma^2/2) + sigma*sqrt(dt)*cr;

s = s0*exp(logRatio);

ssq = s.^2;

plot(Vect',ssq');

% Plot discrete sample paths

% test timescale invariance

clear all;

close all;

clc;

seed = rng;

%%%%%%%%% Problem parameters 

%%%%%%%%%%% 

S = 1; 

mu = 0.05; 

sigma = 0.2; 

L = 1e2; 

T = 1e-3; 

dt = T/L; 

M = 1e1; 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

tvals = [0:dt:T];

% Hint: cumprod, cumulative product

Svals = S*cumprod(exp((mu-0.5*sigma^2)*dt + sigma*(dt)^(1/4)*randn(M,L)),2); 

Svals = [S*ones(M,1) Svals]; 

% add initial asset price

figure;

plot(tvals,Svals);

title([num2str(M) ' asset paths']);

xlabel('t'), ylabel('S(t)')

% Plot discrete sample paths

% test timescale invariance

clear all;

close all;

clc;

seed = rng;

%%%%%%%%% Problem parameters 

%%%%%%%%%%% 

S = 1; 

mu = 0.05; 

sigma = 0.2; 

L = 1e2; 

T = 1e-3; 

dt = T/L; 

M = 1e1; 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

tvals = [0:dt:T];

% Hint: cumprod, cumulative product

Svals = S*cumprod(exp((mu-0.5*sigma^2)*dt + sigma*dt*randn(M,L)),2); 

Svals = [S*ones(M,1) Svals]; 

% add initial asset price

figure;

plot(tvals,Svals);

title([num2str(M) ' asset paths']);

xlabel('t'), ylabel('S(t)')

e1=20;

e3=40;

e2=(e1+e3)/2;

s=linspace(0,80,1000);

plot(s,max(s-e1,0),'b');

hold on; 

plot(s,max(s-e3,0),'b');

hold on;

plot(s,max(s-e1,0)+max(s-e3,0)-2*max(s-e2,0),'r');

hold on;

em=max(max(s-e1,0)+max(s-e3,0)-2*max(s-e2,0));

plot(line([e2,e2],[em,0]));

xlabel('S(T)');

ylabel('V(T)')

title('Payoff of hw1');

axis([0 80 0 40]);

text(20,1,'E1');

text(30,1,'E2');

text(40,1,'E3');

function [C, Cdelta, Cgamma, Cvega, Crho, Ctheta, P, Pdelta, Pgamma, Pvega, Prho, Ptheta] = lect7_1(S,E,r,sigma,tau)

%

%

% Program for Chapter 10 This is a MATLAB function

% Input arguments: S = asset price at time t E = exercise price

% r = interest rate

% sigma = volatility

% tau = time to expiry (T-t)

% Output arguments: C = call value, Cdelta = delta value of call Cvega = vega value of call

% P = Put value, Pdelta = delta value of put Pvega = vega value of put

% function [C, Cdelta, Cvega, P, Pdelta, Pvega] = lect7_1(S,E,r,sigma,tau)

% 

S=1,E=1.5,r=0.05,sigma=0.2,tau=1; 

if tau > 0

    d1 = (log(S/E) + (r + 0.5*sigma^2)*(tau))/(sigma*sqrt(tau)); 

    d2 = d1 - sigma*sqrt(tau);

    N1 = 0.5*(1+erf(d1/sqrt(2)));

    N2 = 0.5*(1+erf(d2/sqrt(2)));

    C = S*N1-E*exp(-r*(tau))*N2;

    Cdelta = N1;

    Cgamma = exp(-0.5*d1^2)/(S*sigma*sqrt(2*pi*tau));

    Cvega = S*sqrt(tau)*exp(-0.5*d1^2)/sqrt(2*pi);

    Crho = tau*E*exp(-r*tau)*N2;

    Ctheta = -S*sigma/(2*sqrt(tau))*exp(-0.5*d1^2)/sqrt(2*pi)- r*E*exp(-r*tau)*N2;

    P = C + E*exp(-r*tau) - S;

    Pdelta = Cdelta - 1;

    Pgamma = Cgamma;

    Pvega = Cvega;

    Prho = Crho - tau*E*exp(-r*tau);

    Ptheta = Ctheta + r*E*exp(-r*tau);

else

    C = max(S-E,0);

    Cdelta = 0.5*(sign(S-E) + 1); 

    Cgamma = 0;

    Cvega = 0;

    Crho = 0;

    Ctheta = 0;

    P = max(E-S,0);

    Pdelta = Cdelta - 1;

    Pgamma = 0;

    Pvega = 0;

    Prho = 0;

    Ptheta = 0;

end

disp([C, Cdelta, Cgamma, Cvega, Crho, Ctheta, P, Pdelta, Pgamma, Pvega, Prho, Ptheta])

 No newline at end of file