Vectorizing

Vectorizing

%% Import test data

    CLC=xlsread('CL.xlsx','CallOptions');

%% plot and compare        
            figure  % CL
            % Call option of CL
            % Bisection methods
             [EstimatedPrice,Interations,CL_B_call_bid]=arrayfun(@bisection_iv,CLC(:,3),CLC(:,1),CLC(:,2),0.0012.*ones(length(CLC),1),0.25.*ones(length(CLC),1));
             subplot(2,2,1);plot(CL_B_call_bid,CLC(:,2)) 
            title('Besection methods implied volatility for call option in CL')
            hold on

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

function [ EstimatedPrice,Interations,ImpliedVolatility ] = bisection_iv(optpx,S,K,r,T) 

%   Using bisection methods to find the implied volatility
% Set the Black Scholers methods to calculate options price

        flag=1;            % Default option type is call
        d1=@(S,K,r,vol,T)(log(S./K)+(r+vol.^2./2).*T)./(vol.*sqrt(T));
        d2=@(S,K,r,vol,T)(log(S./K)+(r-vol.^2./2).*T)./(vol.*sqrt(T));
        bscallpx=@(S,K,r,vol,T)S.*cdf('norm',d1(S,K,r,vol,T))-K.*exp(-r.*T).*cdf('norm',d2(S,K,r,vol,T));
        bsputpx=@(S,K,r,vol,T)K.*exp(-r.*T).*cdf('norm',-d2(S,K,r,vol,T))-S.*cdf('norm',-d1(S,K,r,vol,T));
        bspx=@(S,K,r,vol,T,flag)flag.*bscallpx(S,K,r,vol,T)+(1-flag).*bsputpx(S,K,r,vol,T);
        %bsvega=@(S,K,r,vol,T)S.*pdf('norm',d1(S,K,r,vol,T)).*sqrt(T);
               
    Threshold=0.000001;
    vol_lb=0;    %   define a lowerbound to guess implied volatility
    vol_ub=2;    %   define a upbound to guess implied volatility

    vol=(vol_ub+vol_lb)./2;
    i=1;        
 
       while(abs(optpx-bspx(S,K,r,vol,T,flag))/optpx>Threshold) % Set the accuracy
               
         if optpx>bspx(S,K,r,vol,T,flag)
            vol_lb=vol;
            vol=(vol+vol_ub)/2;
         else
            vol_ub=vol;
            vol=(vol+vol_lb)/2;
         end
          i=i+1;

       end
        EstimatedPrice=bspx(S,K,r,vol,T,flag); 
        Interations=i;
        ImpliedVolatility=vol;
end