This post is just to demonstrate how to replicate the Calculations behind the CBOE Volatility Index, Commonly called VIX. It is also commonly thought of investor gauge of fear. One can read more about at www.cboe.com
The Implementation below follows the methodology as illustrated in the following white paper:
http://www.cboe.com/micro/vix/vixwhite.pdf
M FILE is here:
http://docs.google.com/Doc?id=ddb2j6dw_12fjk57bfx
CODE Published Here:
%% ReplicateVIX
% Near-Term
% Strike Call Put
Data{1} = [775 125.48 0.11;...
800 100.79 0.41;...
825 76.70 1.30;...
850 54.01 3.60;...
875 34.05 8.64;...
900 18.41 17.98;...
925 8.07 32.63;...
950 2.68 52.33;...
975 0.62 75.16;...
1000 0.09 99.61;...
1025 0.01 124.52];
% Next Term
% Strike Call Put
Data{2} = [775 128.78 2.72;...
800 105.85 4.76;...
825 84.14 8.01;...
850 64.13 12.97;...
875 46.38 20.18;...
900 31.40 30.17;...
925 19.57 43.31;...
950 11.00 59.70;...
975 5.43 79.10;...
1000 2.28 100.91;...
1025 0.78 124.38];
%Time_To_Maturity
TM = [16;44];
%Risk_Free_Rate
Rf = 1.1625/100; %Per Annum
% Difference between Calls and Puts (Absolute Value)
DF{1} = abs(Data{1}(:,2) - Data{1}(:,3));
DF{2} = abs(Data{2}(:,2) - Data{2}(:,3));
% Current Time
CT = '08:30:00';
% FInd Hour, Minute, Second from the time using datevec function
[Year, Month, Day, Hour, Minute, Second] = datevec(CT);
%In Years
%1440 is the number of minutes in a day and 510 is the number of minutes to 8:30 AM which
%is the time the option expires on its expiration date
NumYears(1) = [1440 - (Hour * 60 + Minute + Second/60) + 510]/(1440 * 365) + [(TM(1) - 2)/365];
NumYears(2) = [1440 - (Hour * 60 + Minute + Second/60) + 510]/(1440 * 365) + [(TM(2) - 2)/365];
% In days
NumDays = NumYears .* 365;
% Find the minimum of the difference in Call and Put
% Prices and Get the corresponding Strike Price.
ATM(1,:) = Data{1}(find(DF{1}==min(DF{1})),:);
ATM(2,:) = Data{2}(find(DF{2}==min(DF{2})),:);
% Calculate Forward Price Level and Referential Strike
% Application of PUT CALL Parity
Level = ATM(:,1) + exp(Rf*NumYears(:)) .* (ATM(:,2) - ATM(:,3));
%Reference Strike
for i = 1:2
Strike = ATM(i,1);
if(ATM(i,2)>=ATM(i,3))
Ref_Strike(i)=ATM(i,1);
else
Ref_Strike(i) = Data{i}(find(Data{i}(:,1) < ATM(i,1),1,'last'),1);
end
% Differences of Strikes
Temp = diff(Data{i}(:,1));
Delta_Strike{i} = [Temp(1);Temp];
%{
? If the strike is above the “reference strike” , use the call price
? If the strike is below the “reference strike” , use the put price
? If the strike equals the “reference strike” , use the average of the call
and put prices
%}
cpval= zeros(size(Data{i},1),1);
cid = find(Data{i}(:,1) > Ref_Strike(i));
cpval(cid) = Data{i}(cid,2);
pid = find(Data{i}(:,1) < Ref_Strike(i));
cpval(pid) = Data{i}(pid,3);
Aid = find(Data{i}(:,1) == Ref_Strike(i));
cpval(Aid) = (Data{i}(Aid,2) + Data{i}(Aid,3))/2;
% Now do the math as given in the paper vixwhite.pdf
vix{i} = Delta_Strike{i} * exp(Rf*NumYears(i)) .* cpval ./(Data{i}(:,1).^2);
Var(i) = (2/NumYears(i)) * sum(vix{i}) - ((Level(i)/Ref_Strike(i) - 1).^2)/NumYears(i);
% Center the data to 30 days
if(i==1)
Term(i) = NumYears(i) * Var(i) * ((NumDays(i+1)-30)/(NumDays(i+1)-NumDays(i)));
elseif(i==2)
Term(i) = NumYears(i) * Var(i) * ((-NumDays(i-1)+30)/(NumDays(i)-NumDays(i-1)));
end
end
% Final Vix Calculation
VIX = sqrt(sum(Term) * 365/30) * 100
