def UpAndOutCallPrototype(Spot):
#look at times
look_at_times = list(np.linspace(start=0, stop=Expiry, num=12))
#generate a path
market_params = {'spot':Spot, 'rate':rate, 'vol':Vol}
path_generator = GeneratorGBM(market_params)
path_generator.generator.set_seed(seed=0)
path_generator.sim_setup(look_at_times)
sum = 0.
Knockout = 108.
for i in range(0,num_paths):
path = path_generator.do_one_path()
# plt.plot(look_at_times,path)
# plt.show()
#Evaluate the payoff for path
#Check if knocks out above barrier
if any(map(lambda(x): x >= Knockout,path)):
this_payoff = 0
else:
#Calc payoff
po = VanillaCall(Strike=Strike)
this_payoff = po.po(path[-1]) #Get last element of path
sum += this_payoff
def AsianPrototype(Spot):
#look at times
look_at_times = list(np.linspace(start=0, stop=Expiry, num=12))
#generate a path
market_params = {'spot':Spot, 'rate':rate, 'vol':Vol}
path_generator = GeneratorGBM(market_params)
path_generator.sim_setup(look_at_times)
sum = 0.
for i in range(0,num_paths):
path = path_generator.do_one_path()
#plt.plot(look_at_times,path)
#plt.show()
#Evaluate the payoff for path
#Average of price - K
average_price = np.mean(path)
#Calc payoff
po = VanillaCall(Strike=Strike)
this_payoff = po.po(average_price)
sum += this_payoff
#Average and discount
price = math.exp(-rate*Expiry)*sum/num_paths
return price
def setUp(self):
#BS analytics
self.Spot = 110.
self.Strike = 110.
self.rate = 0.05
self.Vol = 0.2
self.dividend = 0.
self.Expiry = 1.
#Setup analytic prices
self.bs1 = af.BSAnalyticFormulas(self.Spot,
self.Strike,
self.rate,
self.Vol,
self.Expiry,
self.dividend)
#Setup MC pricer
num_paths = 100000
times = [self.Expiry]
market_params = {'spot': self.Spot,
'rate': self.rate,
'vol': self.Vol}
generator = GeneratorGBM(market_params)
generator.sim_setup(times)
gatherer = MeanGatherer()
self.van_mc = VanillaMCPricer(spot=self.Spot,
rate=self.rate,
Vol=self.Vol,
generator=generator,
gatherer=gatherer,
num_paths=num_paths,
dividend=0)
def test_UpAndOut_pricer(self):
"""
test that path dependent pricer works for up and out option
with discrete barrier data
"""
num_paths = 500000
#Construct option
barrier = 108.
payoff = VanillaCall(Strike=self.Strike)
#look at times
look_at_times = list(np.linspace(start=0, stop=self.Expiry, num=12))
option_parameters = {
'payoff': payoff,
'look_at_times': look_at_times,
'Expiry': self.Expiry,
'Barrier': barrier
}
ao = UpAndOutCall(option_parameters)
#Construct market parameters for path generation
market_params = {'spot': self.Spot, 'rate': self.rate, 'vol': self.Vol}
path_generator = GeneratorGBM(market_params)
#Construct Pricer parameters
#Note includes path generator
gatherer = SDGatherer()
pricer_parameters = {
'path_generator': path_generator,
'num_paths': num_paths,
'gatherer': gatherer
}
#Contruct pricer
pd_pricer = PathDependentMCPricer(pricer_parameters)
#Do trade
price = pd_pricer.do_trade(ao)
print "MC up and out call price ", price
self.assertAlmostEqual(first=0.2096, second=price,
places=2) #, msg, delta)
def test_AsianArithmetic_pricer(self):
"""
test that asian arithmetic option pricer works
"""
num_paths = 500000
payoff = VanillaCall(Strike=self.Strike)
#look at times
look_at_times = list(np.linspace(start=0, stop=self.Expiry, num=12))
#Contruct Option
option_parameters = {
'payoff': payoff,
'look_at_times': look_at_times,
'Expiry': self.Expiry
}
ao = AsianArithmeticOption(option_parameters)
#Construct market parameters for path generation
market_params = {'spot': self.Spot, 'rate': self.rate, 'vol': self.Vol}
path_generator = GeneratorGBM(market_params)
#Construct Pricer parameters
#Note includes path generator
gatherer = SDGatherer()
pricer_parameters = {
'path_generator': path_generator,
'num_paths': num_paths,
'gatherer': gatherer
}
#Contruct pricer
pd_pricer = PathDependentMCPricer(pricer_parameters)
#Do trade
price = pd_pricer.do_trade(ao)
print "MC Asian opt price ", price
self.assertAlmostEqual(first=2.015, second=price,
places=2) #, msg, delta)
vo_call = VanillaOption(Expiry, PayOff=vc1)
vo_put = VanillaOption(Expiry, PayOff=vp1)
#Model/Market parameters
Spot = 100.
rate = 0.05
Vol = 0.2
dividend = 0.0 #not included in pricing yet
#Model parameters
times = [1.]
num_paths = 50000
market_params = {'spot': Spot, 'rate': rate, 'vol': Vol}
generator = GeneratorGBM(market_params)
generator.sim_setup(times)
gatherer = MeanGatherer()
#Do sim
mc_pricer = VanillaMCPricer(Spot, rate, Vol, generator, gatherer,
num_paths, dividend)
mc_pricer.do_trade(vo_put)
price_put = mc_pricer.price
mc_pricer.do_trade(vo_call)
price_call = mc_pricer.price
#Compare to Analytic Pricer
bsan = BSAnalyticFormulas(Spot, Strike, rate, Vol, Expiry, dividend)
print "MC price Put: ", price_put
vo_put = VanillaOption(Expiry, PayOff=vp1)
#Model/Market parameters
Spot = 100.
rate = 0.05
Vol = 0.2
dividend = 0.0 #not included in pricing yet
#Model parameters
times = [1.]
num_paths = 50000
market_params = {'spot':Spot,
'rate': rate,
'vol': Vol}
generator = GeneratorGBM(market_params)
generator.sim_setup(times)
gatherer = MeanGatherer()
#Do sim
mc_pricer = VanillaMCPricer(Spot, rate, Vol, generator, gatherer, num_paths, dividend)
mc_pricer.do_trade(vo_put)
price_put = mc_pricer.price
mc_pricer.do_trade(vo_call)
price_call = mc_pricer.price
#Compare to Analytic Pricer
bsan = BSAnalyticFormulas(Spot, Strike, rate, Vol, Expiry, dividend)
print "MC price Put: ", price_put
print "Analytic Put price: ", bsan.PutPrice()