Question

刚开始使用matlab编写代码，因为我正在研究Higham的书金融期权评估简介。他给出的示例代码块之一（this is the source）是：

V = zeros(M,1);                                                                 
Vanti = zeros(M,1);                                                             
for i = 1:M                                                                     
    samples = randn(N,1);                                                       

    % standard Monte Carlo                                                      
    Svals = S*cumprod(exp((r-0.5*sigma^2)*Dt+sigma*sqrt(Dt)*samples));          
    Smax = max(Svals);                                                          
    if Smax < B                                                                 
       V(i) = exp(-r*T)*max(Svals(end)-E,0);                                    
    end                                                                         

    % antithetic path                                                           
    Svals2 = S*cumprod(exp((r-0.5*sigma^2)*Dt-sigma*sqrt(Dt)*samples));         
    Smax2 = max(Svals2);                                                        
    V2 = 0;                                                                     
    if Smax2 < B                                                                
       V2 = exp(-r*T)*max(Svals2(end)-E,0);                                     
    end                                                                         
    Vanti(i) = 0.5*(V(i) + V2);                                                 

end

我试图让这个循环更有效率，所以我试图删除for循环。这是我到目前为止写的：

V = zeros(M,1);                                                                 
Vanti = zeros(M,1);                                                             
samples = randn(N,M);                                                           
Svals = S*cumprod(exp((r-0.5*sigma^2)*Dt+sigma*sqrt(Dt)*samples));              
Svals2 = S*cumprod(exp((r-0.5*sigma^2)*Dt-sigma*sqrt(Dt)*samples));             
Send = Svals(end,:);                                                            
Send2 = Svals2(end,:);                                                          
Smax = max(Svals);                                                              
Smax2 = max(Svals2);                                                            
V2 = zeros(M,1);                                                                   
for i = 1:M                                                                        
    if Smax(i) < B                                                                 
       V(i) = exp(-r*T)*max(Send(i)-E,0);                                          
    end                                                                            
    if Smax2(i) < B                                                                
       V2(i) = exp(-r*T)*max(Send2(i)-E,0);                                        
    end                                                                            

end                                                                                
Vanti = 0.5*(V + V2);                                                              
aM = mean(V); bM = std(V);                                                         
conf = [aM - 1.96*bM/sqrt(M), aM + 1.96*bM/sqrt(M)]                                
aManti = mean(Vanti); bManti = std(Vanti);                                                                             
confanti = [aManti - 1.96*bManti/sqrt(M), aManti + 1.96*bManti/sqrt(M)]         
toc

这已经使代码显着更快，因为在循环内部没有生成任何randn变量。但是，我不知道如何删除循环的其他部分。它甚至可能吗？

使matlab代码更有效率

0 个答案: