Barrier Pricer

barrier.py

from random import random
from math import sqrt, log, exp

def box_muller_rand():
    while True:
        x = random() * 2.0 - 1
        y = random() * 2.0 - 1
        d = x * x + y * y 
        if d < 1:
            return x * sqrt(-2 * log(d) / d)

def create_path(initial, time, steps, volatility, risk_free):
    dt = time / steps
    sdt = sqrt(dt)

    path = []
    current = initial
    for i in range(steps):
        path.append(current)
        current = current * exp((risk_free - 0.5 * volatility * volatility) * dt + volatility * sdt * box_muller_rand())
    
    return path

def price_option(strike, spot, time, volatility, risk_free, call_or_put='c', knockin=None, knockout=None, simulations=2000, steps_per_unit = 365):
    if knockin and knockout:
        raise Exception("Unable to cope with 2 barriers!")

    cp = 1 if call_or_put == 'c' else -1

    premiums = []
    for i in range(simulations):
        path = create_path(spot, time, time * steps_per_unit, volatility, risk_free)
        if knockin and knockin > spot and max(path) < knockin: # Up and In
            premiums.append(0)
        elif knockin and knockin < spot and min(path) > knockin: # Down and In
            premiums.append(0)
        elif knockout and knockout < spot and min(path) < knockin: # Down and Out
            premiums.append(0)
        elif knockout and knockout > spot and max(path) > knockout: # Up and Out
            premiums.append(0)
        else:
            premiums.append(max(0, cp * (path[-1] - strike)))

    return sum(premiums) / simulations * exp(-time * risk_free)

spot=100
strike=105
vol=0.2
risk_free=0.05
price_option(strike, spot, 1, vol, risk_free, simulations=50000)