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• 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
  
• # Óöþ·Ö·¨Çóimplied volatility£¬ÔÝÖ»Õë¶Ôcall 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