Replicate a density plot?! How To?
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Hey there,
I have read the paper "The Heston Model A Practical Approach von Moodley (2005)". On page 3 there is the following plot of a density. It shows how the density changes, with a change in the parameter rho:
The Code given is the following:
S0 = 10; V0 = .01; r = 0; k = 2;
theta =.01; sigma= .1; delT = .02; rho =-0.9;
numberOfSimulations = 1000000;
i = 1:numberOfSimulations;
NormRand1 = randn(1,numberOfSimulations);
NormRand2 = randn(1,numberOfSimulations);
S = zeros(1,numberOfSimulations);
V = zeros(1,numberOfSimulations);
V(i) = V0 + k*(theta - V0)*delT + sigma*sqrt(V0)* ...
(rho*NormRand1 + sqrt(1- rho^2)*NormRand2)*sqrt(delT);
V = abs(V); %prevents negative volatilities
S(i) = S0 + r*S0*delT + S0*V.^(0.5).*NormRand1*sqrt(delT);
Nothing more is given than this code. But i dont get how to build it, with this code? Maybe someone can help me with it.
kind regards david
采纳的回答
Geoff Hayes
2015-2-25
David - remember what the density function is. If you look at the minimum and maximum of the S array you will notice that these values (respectively) fall around 9.5 and 10.5. What the author probably did was to create a histogram of the data (from S) and then plot the results to get the figure. Something like
figure;
hold on;
S0 = 10; V0 = .01; r = 0; k = 2;
theta =.01; sigma= .1; delT = .02;
numberOfSimulations = 1000000;
i = 1:numberOfSimulations;
NormRand1 = randn(1,numberOfSimulations);
NormRand2 = randn(1,numberOfSimulations);
S = zeros(1,numberOfSimulations);
V = zeros(1,numberOfSimulations);
for k=1:3
switch k
case 1
rho = 0.9;
ls = '-k';
case 2
rho = 0.0;
ls = '--r';
case 3
rho = -0.9;
ls = '-.b';
end
V(i) = V0 + k*(theta - V0)*delT + sigma*sqrt(V0)* ...
(rho*NormRand1 + sqrt(1- rho^2)*NormRand2)*sqrt(delT);
V = abs(V); %prevents negative volatilities
S(i) = S0 + r*S0*delT + S0*V.^(0.5).*NormRand1*sqrt(delT);
[nelements,centers] = hist(S,50);
plot(centers,nelements/sum(nelements),ls);
end
The majority of the above code is what you already have. The for loop allows us to calculate S for different rho and then plot the results. Note the
[nelements,centers] = hist(S,50);
sorts the data in 50 bins whose centres are given by centers with nelements per bin. We then plot the result as
plot(centers,nelements/sum(nelements),ls);
The above divides by sum(elements) to give a reasonable approximation to the figure.
1 个评论
Geoff Hayes
2015-2-25
David's answer moved here
Hi Geoff,
I can't test it now but after work I will. Thank you so so much in advance :)! You See I am a newbie with Matlab (Never done it before). But with a little help I will get through it.
Regards David
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