def calcOption(S, r, sigma, T, K, NumOftimeStep, NumOfSimulation, callput, rnds = []):
dt = T / NumOftimeStep
payoffs = []
delta = []
vega = []
rho = []
theta = []
for simIndex in range(0, NumOfSimulation):
#For price calculation
rnd = []
stockPath = []
stockPath.append(S)
for stepIndex in range(0, NumOftimeStep):
if len(rnds) is not 0 :
rnd.append(rnds[simIndex][stepIndex])
else :
rnd.append(random.gauss(0, 1))
stockPath.append(AAD_Adjoint_EuropeanVanilla.genStockPath(stockPath[stepIndex], r, sigma, dt, rnd[stepIndex]))
#print rnd[stepIndex], stockPath[stepIndex], S_dot_delta[stepIndex]
#print len(rnd), len(stockPath), len(S_dot_delta)
payoffs.append(AAD_Adjoint_EuropeanVanilla.calcPayoff(stockPath[NumOftimeStep], r, T, K, callput))
#print payoffs[simIndex]
#For greeks calculation
flag = 0
if callput == 'C' :
flag = 1 if stockPath[NumOftimeStep] > K else 0
elif callput == 'P' :
flag = -1 if stockPath[NumOftimeStep] < K else 0
S_bar = math.exp(-r * T) * flag
r_bar = -math.exp(-r * T) * T * flag * (stockPath[NumOftimeStep] - K)
sigma_bar = 0
T_bar = math.exp(-r * T) * flag * (stockPath[NumOftimeStep] - K) * r
K_bar = - math.exp(-r * T) * flag
for stepIndex in range(NumOftimeStep - 1, 0, -1):
#print stepIndex
r_bar = r_bar + stockPath[stepIndex] * dt * S_bar
sigma_bar = sigma_bar + stockPath[stepIndex] * math.sqrt(dt) * rnd[stepIndex] * S_bar
T_bar = T_bar - (r * stockPath[stepIndex] + 0.5 * sigma * stockPath[stepIndex] * rnd[stepIndex] / math.sqrt(dt)) * S_bar / NumOftimeStep
S_bar = (1 + r * dt + sigma * math.sqrt(dt) * rnd[stepIndex]) * S_bar
delta.append(S_bar)
vega.append(sigma_bar)
rho.append(r_bar)
theta.append(T_bar)
price = numpy.average(payoffs)
print "Price: " + repr(price)
print "Delta: " + repr(numpy.average(delta))
print "Vega: " + repr(numpy.average(vega))
print "Rho: " + repr(numpy.average(rho))
print "Theta: " + repr(numpy.average(theta))
def calcOption(S, r, sigma, T, K, NumOftimeStep, NumOfSimulation, callput, rnds = []):
dt = T / NumOftimeStep
payoffs = []
delta = []
vega = []
rho = []
theta = []
for simIndex in range(0, NumOfSimulation):
#For price calculation
rnd = []
stockPaths = []
stockPaths.append(S)
#For greeks calculation
S_dot_delta = []
S_dot_vega = []
S_dot_rho = []
S_dot_theta = []
S_dot_delta.append(1)
S_dot_vega.append(0)
S_dot_rho.append(0)
S_dot_theta.append(0)
for stepIndex in range(0, NumOftimeStep):
if len(rnds) is not 0 :
rnd.append(rnds[simIndex][stepIndex])
else :
rnd.append(random.gauss(0, 1))
stockPaths.append(AAD_Tangent_EuropeanVanilla.genStockPath(stockPaths[stepIndex], r, sigma, dt, rnd[stepIndex]))
S_dot_delta.append(AAD_Tangent_EuropeanVanilla.calcSenOfStockPath(stockPaths[stepIndex], r, sigma, dt, rnd[stepIndex], NumOftimeStep, S_dot_delta[stepIndex], 0, 0, 0))
S_dot_vega.append(AAD_Tangent_EuropeanVanilla.calcSenOfStockPath(stockPaths[stepIndex], r, sigma, dt, rnd[stepIndex], NumOftimeStep,S_dot_vega[stepIndex], 0, 1, 0))
S_dot_rho.append(AAD_Tangent_EuropeanVanilla.calcSenOfStockPath(stockPaths[stepIndex], r, sigma, dt, rnd[stepIndex], NumOftimeStep,S_dot_rho[stepIndex], 1, 0, 0))
S_dot_theta.append(AAD_Tangent_EuropeanVanilla.calcSenOfStockPath(stockPaths[stepIndex], r, sigma, dt, rnd[stepIndex], NumOftimeStep,S_dot_theta[stepIndex], 0, 0, 1))
#print rnd[stepIndex], stockPaths[stepIndex], S_dot_delta[stepIndex]
#print len(rnd), len(stockPaths), len(S_dot_delta)
#def calcPayoffSen(S, r, T, K, S_dot_delta, K_dot, r_dot, T_dot):
payoffs.append(AAD_Tangent_EuropeanVanilla.calcPayoff(stockPaths[NumOftimeStep], r, T, K, callput))
delta.append(AAD_Tangent_EuropeanVanilla.calcPayoffSen(stockPaths[NumOftimeStep], r, T, K, S_dot_delta[NumOftimeStep], 0, 0, 0, callput))
vega.append(AAD_Tangent_EuropeanVanilla.calcPayoffSen(stockPaths[NumOftimeStep], r, T, K, S_dot_vega[NumOftimeStep], 0, 0, 0, callput))
rho.append(AAD_Tangent_EuropeanVanilla.calcPayoffSen(stockPaths[NumOftimeStep], r, T, K, S_dot_rho[NumOftimeStep], 0, 1, 0, callput))
theta.append(AAD_Tangent_EuropeanVanilla.calcPayoffSen(stockPaths[NumOftimeStep], r, T, K, S_dot_theta[NumOftimeStep], 0, 0, 1, callput))
#print payoffs[simIndex]
price = numpy.average(payoffs)
print "Price: " + repr(price)
print "Delta: " + repr(numpy.average(delta))
print "Vega: " + repr(numpy.average(vega))
print "Rho: " + repr(numpy.average(rho))
print "Theta: " + repr(numpy.average(theta))
def calcOption(self, S, r, sigma, T, K, NumOftimeStep, NumOfSimulation, callput):
dt = T / NumOftimeStep
payoffs = []
for simIndex in range(0, NumOfSimulation):
#For price calculation
rnd = []
stockPaths = []
stockPaths.append(S)
for stepIndex in range(0, NumOftimeStep):
if self.rndFlag is True :
rnd.append(self.rnds[simIndex][stepIndex])
else :
rnd.append(random.gauss(0, 1))
stockPaths.append(self.genStockPath(stockPaths[stepIndex], r, sigma, dt, rnd[stepIndex]))
#print rnd[stepIndex], stockPaths[stepIndex], S_dot_delta[stepIndex]
#print len(rnd), len(stockPaths), len(S_dot_delta)
#def calcPayoffSen(S, r, T, K, S_dot_delta, K_dot, r_dot, T_dot):
payoffs.append(self.calcPayoff(stockPaths[NumOftimeStep], r, T, K, callput))
#print payoffs[simIndex]
if self.rndFlag is False :
self.rnds.append(rnd)
price = numpy.average(payoffs)
if self.rndFlag is False : self.rndFlag = True
return price
