1 from math import log,sqrt,exp
2 from scipy import stats
3
4 def bsm_call_value(S0,K,T,r,sigma):
5 S0 = float(S0)
6 d1 = (log(S0 / K) + (r + 0.5 * sigma ** 2) * T) / (sigma * sqrt(T))
7 d2 = (log(S0 / K) + (r - 0.5 * sigma ** 2) * T) / (sigma * sqrt(T))
8 value = (S0 * stats.norm.cdf(d1,0.0,1.0) - K * exp(-r * T) * stats.norm.cdf(d2,0.0,1.0))
9 print value
10 return value
11
12 def bsm_vega(S0,K,T,r,sigma):
13 S0 = float(S0)
14 d1 = (log(S0 / K) + (r + 0.5 * sigma ** 2) * T) / (sigma * sqrt(T))
15 vega = S0 * stats.norm.cdf(d1,0.0,1.0) * sqrt(T)
16 return vega
17
18 def bsm_call_imp_vol(S0,K,T,r,C0,sigma_est,it = 100):
19 for i in range(it):
20 sigma_est -= ((bsm_call_value(S0,K,T,r,sigma_est) - C0) / bsm_vega(S0,K,T,r,sigma_est))
21 print sigma_est
22 return sigma_est
23
24 S0 = 100
25 K = 105
26 T = 1.0
27 r = 0.05
28 sigma = 0.2
29 bsm_call_value(S0,K,T,r,sigma)
