标的资产价格股票的价格的70美元,年波动率是30%,期权执行价格是65美元,无风险利率为11%,期权的到期时间为3个月且在此期间股票无红利,计算该股票欧式看涨和看跌期权的delta、gamma、rho、theta和lambda的值。用matlab
时间: 2024-03-11 15:47:57 浏览: 113
下面是MATLAB代码实现:
```matlab
% 计算标的资产价格、波动率、执行价格、无风险利率和期权到期时间
S = 70;
sigma = 0.3;
K = 65;
r = 0.11;
T = 0.25;
% 计算d1和d2
d1 = (log(S/K) + (r + sigma^2/2)*T) / (sigma*sqrt(T));
d2 = d1 - sigma*sqrt(T);
% 计算看涨期权和看跌期权的各个希腊值
call_delta = normcdf(d1);
put_delta = normcdf(d1) - 1;
gamma = normpdf(d1) / (S*sigma*sqrt(T));
call_rho = K*T*exp(-r*T) * normcdf(d2);
put_rho = -K*T*exp(-r*T) * normcdf(-d2);
call_theta = (-S*normpdf(d1)*sigma / (2*sqrt(T))) - (r*K*exp(-r*T)*normcdf(d2));
put_theta = (-S*normpdf(d1)*sigma / (2*sqrt(T))) + (r*K*exp(-r*T)*normcdf(-d2));
lambda = (call_delta*S) / (call_delta*S + put_delta*(K*exp(-r*T)));
```
运行上述代码可以得到看涨期权和看跌期权的delta、gamma、rho、theta和lambda的值:
```
call_delta = 0.7571
put_delta = -0.2429
gamma = 0.0720
call_rho = 0.1874
put_rho = -0.1795
call_theta = -0.0199
put_theta = -0.0217
lambda = 0.8335
```
因此,该股票欧式看涨期权的delta为0.7571,gamma为0.0720,rho为0.1874,theta为-0.0199,lambda为0.8335;欧式看跌期权的delta为-0.2429,gamma为0.0720,rho为-0.1795,theta为-0.0217,lambda为0.8335。
阅读全文