def SimpleMC1(option,
spot,
vol,
r,
numPaths):
expiry = option.expiry
variance = vol * vol * expiry
rootVariance = np.sqrt(variance)
itoCorrection = -0.5 * variance
movedSpot = spot * np.exp(r * expiry * itoCorrection)
runningSum = 0.
for g in [gaussianBoxMuller() for n in range(numPaths)]:
thisSpot = movedSpot * np.exp(rootVariance * g)
runningSum += option.payoff(thisSpot)
mean = (runningSum / numPaths) * np.exp(-r*expiry)
return mean
def SimpleMC(expiry,
strike,
spot,
vol,
r,
numPaths):
variance = vol * vol * expiry
rootVariance = np.sqrt(variance)
itoCorrection = -0.5 * variance
movedSpot = spot * np.exp(r * expiry * itoCorrection)
thisPayoff = lambda x: 0 if x <= strike else x - strike
runningSum = 0.
for g in [gaussianBoxMuller() for n in range(numPaths)]:
thisSpot = movedSpot * np.exp(rootVariance * g)
runningSum += thisPayoff(thisSpot)
mean = (runningSum / numPaths) * np.exp(-r*expiry)
return mean
