Adv Calc HW 3 | Python Fiddle

""" AUTHOR JONATHAN LAU"""

import math

"""
The following is the cdf of a standard normal variable 
    
"""

def f(x):
    return math.exp((-x**2.0)/2.0)

def simp_rule(a, b, n):
    h = (b-a)/float(n)
    total = f(a) / 6.0 + f(b) / 6.0
    
    for i in range (1, n):
        total = total + f(a + i*h) / 3.0
        
    for i in range (1, n+1):
        total = total + 2 * f(a + (i-0.5) * h) / 3.0
        
    return total * h

def cum_distrib(x, n):
    total = 0.5
    return total + 1/(math.sqrt(2.0 * math.pi)) * simp_rule(0.0, x, n)

def cum_distrib_tol(tol, x):
    tolerance = float(tol)
    n = 4
    old_int = cum_distrib(x,n)
    n = 2 * n
    new_int = cum_distrib(x,n)
    
    while abs(new_int - old_int) > tolerance:
        old_int = new_int
        n = 2* n
        new_int = cum_distrib(x,n)
    
    return new_int
"""return (n, new_int, abs(new_int - old_int) ) ==> copy this in if you want to see how many iterations it takes, and what the difference between the new and old estimates are"""

""" Black Scholes Theorem"""

def PutCallOptionPrice (S, K, r, q, vol, T, t):
    d1 = ( math.log(float(S) / K) + (r - q + (vol**2)/2) * (T - t) ) / (vol * math.sqrt(T - t))
    d2 = d1 - vol * math.sqrt(T - t)
    
    C = S* math.exp(-q* (T-t)) * cum_distrib_tol(10**-12, d1) - K * math.exp(-r *(T-t)) * cum_distrib_tol(10**-12, d2)
    P = K* math.exp(-r* (T-t)) * cum_distrib_tol(10**-12, -d2) - S * math.exp(-q *(T-t)) * cum_distrib_tol(10**-12, -d1)
    
    return (C, P, d1, d2)

print PutCallOptionPrice(60, 50, 0.01, 0.02, 0.2, 0.75, 0)
print PutCallOptionPrice(20, 40, 0.02, 0.03, 0.3, 0.25, 0)
print PutCallOptionPrice(42.0, 40.0, 0.05, 0.03, 0.3, 0.5, 0.0)
print cum_distrib_tol(10**-12, 2)

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