def main():
"""Set up the option!"""
strike = 40.0
expiry = .25
"""Set up the Market Data!"""
spot = 41.0
rate = 0.08
volatility = 0.30
dividend = 0.0
"""Set up the European Binomial Pricing Engine!"""
steps = 500
call = VanillaPayoff(expiry, strike, call_payoff)
data = MarketData(rate, spot, volatility, dividend)
binom_engine = BinomialPricingEngine(steps, EuropeanBinomialPricer)
"""Calculate the Price"""
the_option = OptionFacade(call, binom_engine, data)
price = the_option.price()
print("The European Binomial Call Price is {0:.3f}".format(price))
"""Set up Black Scholes Price!"""
the_call = VanillaPayoff(expiry, strike, call_payoff)
BS_engine = BlackScholesPricingEngine("call", BlackScholesPricer)
BS_option = OptionFacade(the_call, BS_engine, data)
BS_price = BS_option.price()
print("The call price via BLack Scholes is: {0:.3f}".format(BS_price))
def main():
strike = 40.0
expiry = .25
spot = 41.0
rate = 0.08
volatility = 0.30
dividend = 0.0
steps = 500
the_call = VanillaPayoff(expiry, strike, call_payoff)
the_data = MarketData(rate, spot, volatility, dividend)
binom_engine = BinomialPricingEngine(steps, EuropeanBinomialPricer)
the_option = OptionFacade(the_call, binom_engine, the_data)
price = the_option.price()
print("The Call Price is {0:.3f}".format(price))
def main():
strike = 40.0
expiry = 0.25
spot = 41.0
rate = 0.08
volatility = 0.30
dividend = 0.0
steps = 3
the_call = VanillaPayoff(expiry, strike, call_payoff)
the_data = MarketData(rate, spot, volatility, dividend)
A_binom_engine = BinomialPricingEngine(steps, AmericanBinomialPricer)
the_option = OptionFacade(the_call, A_binom_engine, the_data)
price = the_option.price()
print("The call price is {0:.3f}".format(price))
def main():
strike = 40.0
expiry = 0.25
spot = 41.0
rate = 0.08
volatility = 0.30
dividend = 0.0
time_steps = 100
replications = 1000
the_call = VanillaPayoff(expiry, strike, call_payoff)
the_data = MarketData(rate, spot, volatility, dividend)
convar_mc_engine = MonteCarloPricingEngine(time_steps, replications, ControlVariatePricer)
the_option = OptionFacade(the_call, convar_mc_engine, the_data)
price = the_option.price()
print("The Call Price via Control Variate Monte Carlo is {0:.3f}".format(price))
def main():
strike = 40.0
expiry = .25
spot = 41.0
rate = 0.08
volatility = 0.30
dividend = 0.0
time_steps = 100
replications = 1000
the_call = VanillaPayoff(expiry, strike, call_payoff)
the_data = MarketData(rate, spot, volatility, dividend)
strat_mc_engine = MonteCarloPricingEngine(time_steps, replications, Stratified_Monte_Carlo_Pricer)
the_option = OptionFacade(the_call, strat_mc_engine, the_data)
price = the_option.price()
print("The Call Price is {0:.3f}".format(price))
def main():
"""Set up the option!"""
expiry = 0.25
strike = 40.0
"""Set up the data!"""
spot = 41.0
rate = 0.08
volatility = 0.30
dividend = 0.0
"""set up the engine!"""
#steps = 500
#type = "Put"
bs_engine = BlackScholesPricingEngine("call", BlackScholesPricer)
the_data = MarketData(rate, spot, volatility, dividend)
the_call = VanillaPayoff(expiry, strike, call_payoff)
option2 = OptionFacade(the_call, bs_engine, the_data)
price2 = option2.price()
print("The call price via Black-Scholes is: {0:.3f}".format(price2))
def main():
"""Set up the option!"""
strike = 40.0
expiry = .25
"""Set up the Market Data!"""
spot = 40.0
rate = 0.08
volatility = 0.30
dividend = 0.0
"""Set up the Pricing Engine!"""
time_steps = 10
replications =10000
call = ExoticPayoff(expiry, strike, arithmetic_asian_call_payoff)
data = MarketData(rate, spot, volatility, dividend)
Arithmetic_A_engine = MonteCarloPricingEngine(time_steps, replications, Asian_Option_Pricer)
AA_option = OptionFacade(call, Arithmetic_A_engine, data)
AA_price = AA_option.price()
print("The call price for an Arithmetic Asian Call Option using a Geometric Asian control Variate is: {0:.3f}".format(AA_price))
def main():
"""Set up the option!"""
strike = 40.0
expiry = .25
"""Set up the Market Data!"""
spot = 41.0
rate = 0.08
volatility = 0.30
dividend = 0.0
"""Set up the European Binomial Pricing Engine!"""
steps = 500
call = VanillaPayoff(expiry, strike, call_payoff)
data = MarketData(rate, spot, volatility, dividend)
binom_engine = BinomialPricingEngine(steps, EuropeanBinomialPricer)
"""Calculate the Price"""
the_option = OptionFacade(call, binom_engine, data)
price = the_option.price()
print("The European Binomial Call Price is {0:.3f}".format(price))
"""Set up Black Scholes Price!"""
the_call = VanillaPayoff(expiry, strike, call_payoff)
BS_engine = BlackScholesPricingEngine("call", BlackScholesPricer)
BS_option = OptionFacade(the_call, BS_engine, data)
BS_price = BS_option.price()
print("The call price via BLack Scholes is: {0:.3f}".format(BS_price))
from probo.payoff import VanillaPayoff, call_payoff, put_payoff
from probo.engine import MonteCarloEngine, lsmPricer
from probo.facade import OptionFacade
## Set up the market data
spot = 1.0
rate = 0.06
volatility = 0.30
dividend = 0.0
thedata = MarketData(rate, spot, volatility, dividend)
## Set up the option
expiry = 3.0
strike = 1.10
thecall = VanillaPayoff(expiry, strike, call_payoff)
theput = VanillaPayoff(expiry, strike, put_payoff)
## Set up Naive Monte Carlo
nreps = 8
steps = 3
pricer = lsmPricer
mcengine = MonteCarloEngine(nreps, steps, pricer)
## Calculate the price
option2 = OptionFacade(theput, mcengine, thedata)
price2 = option2.price()
print("The put price via Least Squares Monte Carlo is: {0:.3f}".format(price2))
return paths paths = AssetPaths(spot, rate, volatility, expiry, dividend, nreps, steps) maxSpot = np.amax(paths[1]) minSpot = np.amin(paths[1]) #------------------------------------------------------------------- #MonteCarlo pricer = NaiveMonteCarloPricer mcengine = MonteCarloEngine(nreps, steps, pricer) ## Calculate the prices startTime1 = time.time() option1 = OptionFacade(thecall, mcengine, thedata) mcCallPrice, mcCallSe = option1.price() endTime1 = time.time() totalTime1 = endTime1 - startTime1 startTime2 = time.time() option2 = OptionFacade(theput, mcengine, thedata) mcPutPrice, mcPutSe = option2.price() endTime2 = time.time() totalTime2 = endTime2 - startTime2 #------------------------------------------------------------------- #Control Variate pricer = ControlVariatePricer
from probo.marketdata import MarketData
from probo.payoff import VanillaPayoff, call_payoff, put_payoff
from probo.engine import MonteCarloEngine, lsmPricer
from probo.facade import OptionFacade
## Set up the market data
spot = 1.0
rate = 0.06
volatility = 0.30
dividend = 0.0
thedata = MarketData(rate, spot, volatility, dividend)
## Set up the option
expiry = 3.0
strike = 1.10
thecall = VanillaPayoff(expiry, strike, call_payoff)
theput = VanillaPayoff(expiry, strike, put_payoff)
## Set up Naive Monte Carlo
nreps = 8
steps = 3
pricer = lsmPricer
mcengine = MonteCarloEngine(nreps, steps, pricer)
## Calculate the price
option2 = OptionFacade(theput, mcengine, thedata)
price2 = option2.price()
print("The put price via Least Squares Monte Carlo is: {0:.3f}".format(price2))
from probo.facade import OptionFacade
## Set up the market data
spot = 100.0
rate = 0.06
volatility = 0.20
dividend = 0.03
thedata = MarketData(rate, spot, volatility, dividend)
## Set up the option
expiry = 1.0
strike = 100.0
thecall = VanillaPayoff(expiry, strike, call_payoff)
#theput = VanillaPayoff(expiry, strike, put_payoff)
## Set up Naive Monte Carlo
nreps = 100
steps = 10
pricer = AsianPricer
mcengine = AsianMonteCarloEngine(nreps, steps, pricer)
## Calculate the price
option1 = OptionFacade(thecall, mcengine, thedata)
price1 = option1.price()
print("The call price via Naive Monte Carlo is: {0:.3f}".format(price1))
## Only works for calls
#option2 = OptionFacade(theput, mcengine, thedata)
#price2 = option2.price()
#print("The put price via Naive Monte Carlo is: {0:.3f}".format(price2))
spot = 41.0
rate = 0.08
volatility = 0.30
dividend = 0.0
thedata = MarketData(rate, spot, volatility, dividend)
## Set up the option
expiry = 1.0
strike = 40.0
thecall = ExoticPayoff(expiry, strike, lookbackCallPayoff)
theput = ExoticPayoff(expiry, strike, lookbackPutPayoff)
## Set up Naive Monte Carlo
nreps = 100000
steps = 252
pricer = NaiveMonteCarloPricer
#pricer = PathwiseNaiveMonteCarloPricer
mcengine = MonteCarloEngine(nreps, steps, pricer)
## Calculate the price
option1 = OptionFacade(thecall, mcengine, thedata)
price1 = option1.price()
print("The call price via Naive Monte Carlo is: {0:.3f}".format(price1[0]))
option2 = OptionFacade(theput, mcengine, thedata)
price2 = option2.price()
print("The put price via Naive Monte Carlo is: {0:.3f}".format(price2[0]))
## Set up the market data
spot = 41.0
rate = 0.08
volatility = 0.30
dividend = 0.0
thedata = MarketData(rate, spot, volatility, dividend)
## Set up the option
expiry = 1.0
strike = 40.0
thecall = VanillaPayoff(expiry, strike, call_payoff)
theput = VanillaPayoff(expiry, strike, put_payoff)
## Set up Naive Monte Carlo
nreps = 100000
steps = 1
pricer = NaiveMonteCarloPricer
mcengine = MonteCarloEngine(nreps, steps, pricer)
## Calculate the price
option1 = OptionFacade(thecall, mcengine, thedata)
price1, se1 = option1.price()
print("The call price via Naive Monte Carlo is: {0:.3f}".format(price1))
option2 = OptionFacade(theput, mcengine, thedata)
price2, se2 = option2.price()
print("The put price via Naive Monte Carlo is: {0:.3f}".format(price2))
spot = 41.0
rate = 0.08
volatility = 0.30
dividend = 0.0
thedata = MarketData(rate, spot, volatility, dividend)
## Set up the option
expiry = 1.0
strike = 40.0
thecall = ExoticPayoff(expiry, strike, arithmeticAsianCallPayoff)
theput = ExoticPayoff(expiry, strike, arithmeticAsianPutPayoff)
## Set up Naive Monte Carlo
nreps = 100000
steps = 1
pricer = NaiveMonteCarloPricer
# pricer = PathwiseNaiveMonteCarloPricer
mcengine = MonteCarloEngine(nreps, steps, pricer)
## Calculate the price
option1 = OptionFacade(thecall, mcengine, thedata)
price1 = option1.price()
print("The call price via Naive Monte Carlo is: {0:.3f}".format(price1))
option2 = OptionFacade(theput, mcengine, thedata)
price2 = option2.price()
print("The put price via Naive Monte Carlo is: {0:.3f}".format(price2))
volatility = 0.30
dividend = 0.0
thedata = MarketData(rate, spot, volatility, dividend)
## Set up the option
expiry = 1.0
strike = 40.0
thecall = VanillaPayoff(expiry, strike, call_payoff)
theput = VanillaPayoff(expiry, strike, put_payoff)
## Set up the European Binomial pricer
steps = 3
pricer = EuropeanBinomialPricer
binomengine = BinomialPricingEngine(steps, pricer)
## Calculate the price
option1 = OptionFacade(thecall, binomengine, thedata)
price1 = option1.price()
print("The call price via European Binomial is: {0:.3f}".format(price1))
option2 = OptionFacade(theput, binomengine, thedata)
price2 = option2.price()
print("The put price via European Binomial is: {0:.3f}".format(price2))
## Set up the Black-Scholes pricer
#bsengine = BlackScholesPricingEngine(BlackScholesPayoffType.call, BlackScholesPricer)
bsengine = BlackScholesPricingEngine("call", BlackScholesPricer)
option3 = OptionFacade(thecall, bsengine, thedata)
price3 = option3.price()
print("The call price via Black-Scholes is: {0:.3f}".format(price3))
dividend = 0.03
thedata = MarketData(rate, spot, volatility, dividend)
## Set up the option
expiry = 1.0
strike = 100.0
thecall = VanillaPayoff(expiry, strike, call_payoff)
theput = VanillaPayoff(expiry, strike, put_payoff)
## Set up Simple Monte Carlo
nreps = 10000
steps = 10
pricer = PathwiseNaiveMonteCarloPricer
call_mcengine = MonteCarloEngine(nreps, steps, pricer, "call")
put_mcengine = MonteCarloEngine(nreps, steps, pricer, "put")
calloption = OptionFacade(thecall, call_mcengine, thedata)
call_price = calloption.price()
print("\nThe call price and standard error via Naive Monte Carlo are: " +
str(call_price))
putoption = OptionFacade(theput, put_mcengine, thedata)
put_price = putoption.price()
print("\nThe put price and standard error via Naive Monte Carlo are: " +
str(put_price))
## control variate
pricer = PathwiseControlVariatePricer
print(
"\nThe call price and standard error via Control Variate Monte Carlo are: "
+ str(call_price))
def main():
"""Set up the option!"""
strike = 40.0
expiry = .25
"""Set up the Market Data!"""
spot = 41.0
rate = 0.08
volatility = 0.30
dividend = 0.0
"""Set up the Pricing Engine!"""
time_steps = 25
replications =500
call = VanillaPayoff(expiry, strike, call_payoff)
data = MarketData(rate, spot, volatility, dividend)
"""Set up Black Scholes Price!"""
the_call = VanillaPayoff(expiry, strike, call_payoff)
BS_engine = BlackScholesPricingEngine("call", BlackScholesPricer)
BS_option = OptionFacade(the_call, BS_engine, data)
BS_price = BS_option.price()
print("The call price via BLack Scholes is: {0:.3f}".format(BS_price))
"""Naive Monte Carlo"""
the_call = VanillaPayoff(expiry, strike, call_payoff)
the_data = MarketData(rate, spot, volatility, dividend)
mc_engine = MonteCarloPricingEngine(replications, time_steps, Naive_Monte_Carlo_Pricer)
the_option = OptionFacade(the_call, mc_engine, the_data)
MC_price = the_option.price()
print("The Naive Monte Carlo Call Price is {0:.3f}".format(MC_price))
"""Antithetic Monte Carlo"""
anti_mc_engine = MonteCarloPricingEngine(replications, time_steps, Antithetic_Monte_Carlo_Pricer)
anti_option = OptionFacade(the_call, anti_mc_engine, the_data)
anti_price = anti_option.price()
print("The Antithetic Monte Carlo Call Price is {0:.3f}".format(anti_price))
"""Stratified Monte Carlo"""
strat_mc_engine = MonteCarloPricingEngine(replications, time_steps, Stratified_Monte_Carlo_Pricer)
strat_option = OptionFacade(the_call, strat_mc_engine, the_data)
strat_price = strat_option.price()
print("The Stratified Monte Carlo Call Price is {0:.3f}".format(strat_price))
"""Control Variate Monte Carlo"""
convar_mc_engine = MonteCarloPricingEngine(replications, time_steps, ControlVariatePricer)
convar_option = OptionFacade(the_call, convar_mc_engine, the_data)
convar_price = convar_option.price()
print("The Call Price via Control Variate Monte Carlo is {0:.3f}".format(convar_price))
rate = 0.06
volatility = 0.2
dividend = 0.03
thedata = MarketData(rate, spot, volatility, dividend)
## Set up the option
expiry = 1.0
strike = 100.0
thecall = VanillaPayoff(expiry, strike, call_payoff)
## Set up Asian Control Variate Pricer
nreps = 10000
steps = 10
pricercontvar = AsianControlVariatePricerCall
enginecontvar = MonteCarloEngine(nreps, steps, pricercontvar)
## Set up Naive Asian Pricer (nreps and nsteps are the same)
pricernaive = NaiveAsianCall
enginenaive = MonteCarloEngine(nreps, steps, pricernaive)
## Calculate the price
option1 = OptionFacade(thecall, enginecontvar, thedata)
price1, se1 = option1.price()
option2 = OptionFacade(thecall, enginenaive, thedata)
price2, se2 = option2.price()
print("The Asian Control Variate Call is {0:.3f}".format(price1),
" The SE is{0:.6f}".format(se1))