Scilab code to estimate Asian call option using the control variates method
Hello everyone,
I need to estimate Asian call option based on the arithmetic mean by using the control variates method. Since we have the exacte value of the option with geometric mean (Black-Scholes formula), i choosed the geometric mean as a control variates for the arithmetic mean.
The problem is that i'm getting the same values (graph) for the confidence interval limits and the estimate values.
Please help me to fix it.
Thanks in advance.
clear;
clc;
K = 120;
S0 = 100;
r = 0.04;
sigma = 0.4;
sigma2 = sigma^2;
T = 1;
n = 52;
dt = T/n;
t = 0:dt:T;
Nmax = 100;
z = 1.96;
sigman=(sigma/n)*sqrt(((n+1)*(2*n+1))/6);
sigman2=sigman^2;
rn=(r-0.5*sigma2)*(0.5*(n+1)/n)+0.5*sigman2;
d1 = (log(S0/K)+(rn+0.5*sigman2)*T)/(sigman*sqrt(T));
d2 = d1-sigman*sqrt(T);
ECg = exp(-r*T)*(S0*exp(rn*T)*cdfnor("PQ",d1,0,1)-K*cdfnor("PQ",d2,0,1));
function S=f(x)
S = ones(1,n);
for i = 1:n
u = exp((r-0.5*sigma2)*t(i+1)+sigma*x*sqrt(t(i+1)));
S(i)= u;
end
endfunction
function [CI_low, CI_up, CV]=integralCV(N)
S1 = 0;
S2 = 0;
for i = 1:N
u = grand(Nmax,1,"nor",0,1);
St = S0 * f(u(1));
ht1 = max(mean(St)-K,0);
ht2 = max((prod(St))^(1/n)-K,0);
ht = ht1-ht2;
S1 = S1 + exp(-r*T)*ht;
S2 = S2 + (exp(-r*T)*ht)^2;
end
CV = S1 / N + ECg;
stdev = sqrt((1 / (N-1))*( S2 - N*CV^2 ));
CI_low = CV - z * stdev / sqrt(N) ;
CI_up = CV + z * stdev / sqrt(N) ;
endfunction
D = 10:1:Nmax-9;
for i=1:length(D)
[CI_lowerCV(i), CI_upperCV(i), CV(i)] = integralCV(D(i));
clf();
plot2d(log10(D)', [ CI_lowerCV CI_upperCV CV], [ 3 5 2 ]);
legend([ "Lower Bound (CV)" "Upper Bound (CV)" "CV"]);
title("Estimation of E[Ca] by the control variates method");
- unanswered
- 197 views
- Pro Bono
Related Questions
- How do I compare categorical data with multiple uneven populations?
- Computing mean, median, inter-quartile range, and standard deviation
- Probability that the distance between two points on the sides of a square is larger than the length of the sides
- Causality Help!?!?
- Intro to stats symmetry vs skew and missing data values questions
- Confidence Interval - Poisson
- Calculating Dependant Probability of Multiple Events
- Joint PDF evaluated over a curve $P_{U,V}$
This is a very advanced problem...