例1_欧式看涨期权

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例1现有一个欧式看涨期权，标的资产为无红利支付的股票。当前股票价格为S=100美元，股票波动率为=0.4，无风险利率为r=0.05，期权的敲定价格为X=95美元，期权有效期为T=0.5。求该期权的价格。

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%欧式期权定价的二叉树方法%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%|输入具体的参数
St=100%当前股价X=95%执行价格r=0.05%利率t=0.5%期权有效期
sigma=0.4%波动率
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%确定二叉树参数
n=10%指定二叉树的步数dt=t/n%确定单步时间间隔u=exp(sigma*sqrt(dt%计算上升比率d=1/u%计算下降比率p=(exp(r*dt-d/(u-d%计算上升概率
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%构造股票价格二叉树矩阵，a表示行数，b表示列数（第b-1步），mx为股价矩阵forb=1:n+1
fora=1:b;
mx(a,b=st*power(u,b–a*power(d,a-1
end;end;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%构造期权价格二叉树矩阵efx
%计算到期(b=n+1时，欧式期权价格efxfora=1:n+1
efx(a,n+1=max(mx(a,n+1–X,0;end

%倒推前面各期的期权价格forbb=1:n
b=n+1–bb;fora=1:b;
efx(a,b=exp(-r*dt*(p*efx(a,b+1+(1-p*efx(a+1,b+1;end;
end;
efx%输出结果运行后得到的结果为

efx=
Columns1through7
15.047321.066628.780738.306249.621762.573976.973109.300213.710419.710627.552037.339348.9591005.08127.975312.224518.222726.28620002.30743.90536.484010.514500000.77351.43062.6182000000.14180.2892000000000000000Columns8through11
92.7399110.003362.104776.501736.487548.487616.550325.06224.72928.40020.58971.2025000000000
0
000092.267261.632036.014814.59372.45200000
00000109.529476.027948.013824.58845.00000000
0
000000000000
128.9034149.5934

例1_欧式看涨期权

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