/
bs.py
69 lines (58 loc) · 2.15 KB
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bs.py
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from scipy.stats import norm
from scipy.optimize import newton
import numpy as np
# s: stock price k: Strike Price
# v: volatility(std) r: risk free rate
# t: time d: contineous dividend yield
def bs(cflag,s,k,v,r,t):
d1=(np.log(s/k)+(r+v*v/2)*t)/(v*np.sqrt(t))
d2=d1-v*np.sqrt(t)
if cflag: # call
return s*norm.cdf(d1) - k*np.exp(-r*t)*norm.cdf(d2)
else: # put
return k*np.exp(-r*t)*norm.cdf(-d2) - s*norm.cdf(-d1)
def delta(cflag,s,k,v,r,t):
d1=(np.log(s/k)+(r+v*v/2)*t)/(v*np.sqrt(t))
if cflag: # call
return norm.cdf(d1)
else: # put
return norm.cdf(-d1) - 1
def gamma(s,k,v,r,t):
d1=(np.log(s/k)+(r+v*v/2)*t)/(v*np.sqrt(t))
return norm.pdf(d1)/(s*v*np.sqrt(t))
def vega(s,k,v,r,t):
d1=(np.log(s/k)+(r+v*v/2)*t)/(v*np.sqrt(t))
return s*norm.pdf(d1)*np.sqrt(t)
def theta(cflag,s,k,v,r,t):
d1=(np.log(s/k)+(r+v*v/2)*t)/(v*np.sqrt(t))
d2=d1-v*np.sqrt(t)
if cflag: # call
return -s*norm.pdf(d1)*v/(2*np.sqrt(t)) - r*k*np.exp(-r*t)*norm.pdf(d2)
else: # put
return -s*norm.pdf(d1)*v/(2*np.sqrt(t)) + r*k*np.exp(-r*t)*norm.pdf(-d2)
def rho(s,k,v,r,t):
return
def impvol(cflag,s,k,r,t,c,guess,tolerance=0.005,maxnum=1000):
sigma = guess
f = lambda x: bs(cflag,s,k,x,r,t)-c
v = lambda y: vega(s,k,y,r,t)
sigma = newton(f,guess,fprime=v,tol=tolerance,maxiter=maxnum)
if sigma <=0:
sigma = 0
elif sigma > 1:
sigma = 0
return sigma
if __name__=="__main__":
# cflag, S, K, v, r, dte, dividend
print "Call:"
print 'price: ',bs(True, 41.,40.,.3,.08,.25)
print 'delta: ',delta(True, 41.,40.,.3,.08,.25)
print 'gamma: ',gamma(41.,40.,.3,.08,.25)
print 'vega: ',vega(41.,40.,.3,.08,.25)
print 'theta: ',theta(True, 41.,40.,.3,.08,.25)
print "\n\nPut:"
print 'price: ',bs(False, 41.,40.,.3,.08,.25)
print 'delta: ',delta(False, 41.,40.,.3,.08,.25)
print 'gamma: ',gamma(41.,40.,.3,.08,.25)
print 'vega: ',vega(41.,40.,.3,.08,.25)
print 'theta: ',theta(False, 41.,40.,.3,.08,.25)