#-----------------------------------------------------------------------
# blackscholes.py
#-----------------------------------------------------------------------

import stdio
import sys
import math

#-----------------------------------------------------------------------

# Return the value of the Gaussian probability function with mean 0.0
# and standard deviation 1.0 at the given x value.

def phi(x):
    return math.exp(-x * x / 2.0) / math.sqrt(2.0 * math.pi)

#-----------------------------------------------------------------------

# Return the value of the Gaussian probability function with mean mu
# and standard deviation sigma at the given x value.

def pdf(x, mu=0.0, sigma=1.0):
    return phi((x - mu) / sigma) / sigma

#-----------------------------------------------------------------------

# Return the value of the cumulative Gaussian distribution function
# with mean 0.0 and standard deviation 1.0 at the given z value.

def Phi(z):
    if z < -8.0: return 0.0
    if z >  8.0: return 1.0
    total = 0.0
    term = z
    i = 3
    while total != total + term:
        total += term
        term *= z * z / float(i)
        i += 2
    return 0.5 + total * phi(z)

#-----------------------------------------------------------------------

# Return standard Gaussian cdf with mean mu and stddev sigma.
# Use Taylor approximation.

def cdf(z, mu=0.0, sigma=1.0):
    return Phi((z - mu) / sigma)

#-----------------------------------------------------------------------

# Black-Scholes formula.

def callPrice(s, x, r, sigma, t):
    a = (math.log(s/x) + (r + sigma * sigma/2.0) * t) / \
        (sigma * math.sqrt(t))
    b = a - sigma * math.sqrt(t)
    return s * cdf(a) - x * math.exp(-r * t) * cdf(b)

#-----------------------------------------------------------------------

# Accept s, x, r, sigma, and t from the command line and write
# the Black-Scholes value.

s     = float(sys.argv[1])
x     = float(sys.argv[2])
r     = float(sys.argv[3])
sigma = float(sys.argv[4])
t     = float(sys.argv[5])

stdio.writeln(callPrice(s, x, r, sigma, t))

#-----------------------------------------------------------------------

# python blackscholes.py 23.75 15.00 0.01 0.35 0.5
# 8.879159263714124   (actual =  9.10)

# $ python blackscholes.py 30.14 15.0 0.01 0.332 0.25
# 15.177462481558178   (actual = 14.50)

# Information calculated based on closing data on Monday, June 9th 2003.
#
# Microsoft:   share price:             23.75
#              strike price:            15.00
#              risk-free interest rate:  1%
#              volatility:              35%      (historical estimate)
#              time until expiration:    0.5 years
#
# GE:          share price:             30.14
#              strike price:            15.00
#              risk-free interest rate   1%
#              volatility:              33.2%    (historical estimate)
#              time until expiration     0.25 years
#
# Reference:  http://www.hoadley.net/options/develtoolsvolcalc.htm