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zyj8119

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[交流] 【原创】一维brown运动在经济学中的应用

资产变化时一个随机过程,因此,了解和掌握这个随机过程的基本特征,是期权定价理论首先要回答的问题。例如,股票价格变动故从几何布朗运动或对数正态分布,是Black和Scholes在推导BS期权定价模型时用到的最基本的假设。生产布朗运动的随机序列,编写了函数BrownM,可以生成一维或者二维的随机序列,具体使用方法为
   function data = BrownM(Npoints,Mean,Std,Opt)
代码如下:
CODE:
function data = BrownM(Npoints,Mean,Std,Opt)
dt=1;
if Opt==1
    %%
%standard Brownian motion
  temp=cumsum(dt^0.5.*random('Normal',0,1,1,1000))
  data=[0,temp];
  figure
  plot(0:Npoints,data);
elseif Opt==2
    figure
    data=cumsum([zeros(1,3);dt^0.5*random(...
    'Normal',Mean,std,1,Npoints-1,3)]);
    plot3(data(:,1),data(:,2),data(:,3),'k');
    pcol=(data-repmat(min(data),Npoints,1))./...
        repmat(max(data)-min(data),Npoints,1);
    hold on;
    scatters(data(:,1),data(:,2),data(:,3),...
        10,pcol,'filled');
    grid on;
    hold off;
else
    error('Opt=1 or Opt=2')
end

运行结果是:
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