Below is the syntax highlighted version of blackscholes.py
from §2.1 Using and Defining Functions.
#----------------------------------------------------------------------- # 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