如何用python计算隐含波动率

如何用python计算隐含波动率

设定参数

r=0.032 # risk-free interest rate

t=float(30)/365 # time to expire (30 days)

q=0 # dividend yield

S0=2.3 # underlying price

X=2.2 # strike price

mktprice=0.18 # market price

# 用二分法求62616964757a686964616fe78988e69d8331333363376539implied volatility，暂只针对call option

sigma=0.3 # initial volatility

C=P=0

upper=1

lower=0

while abs(C-mktprice)>1e-6:

d1=(np.log(S0/X)+(r-q+sigma**2/2)*t)/(sigma*np.sqrt(t))

d2=d1-sigma*np.sqrt(t)

C=S0*np.exp(-q*t)*norm.cdf(d1)-X*np.exp(-r*t)*norm.cdf(d2)

P=X*np.exp(-r*t)*norm.cdf(-d2)-S0*np.exp(-q*t)*norm.cdf(-d1)

if C-mktprice>0:     

upper=sigma  

sigma=(sigma+lower)/2

else:       

lower=sigma     

sigma=(sigma+upper)/2

print sigma # implied volatility

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