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PRDC.py
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PRDC.py
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import numpy as np
import QuantLib as ql
class PathGenerator:
def __init__(self, valuation_date, coupon_schedule, day_counter, process):
self.valuation_date = valuation_date
self.coupon_schedule = coupon_schedule
self.day_counter = day_counter
self.process = process
#
self.create_time_grids()
def create_time_grids(self):
all_coupon_dates = np.array(self.coupon_schedule)
remaining_coupon_dates = all_coupon_dates[all_coupon_dates > self.valuation_date]
self.time_grid = np.array([self.day_counter.yearFraction(self.valuation_date, date)
for date in remaining_coupon_dates])
self.time_grid = np.concatenate((np.array([0.0]), self.time_grid))
self.grid_steps = np.diff(self.time_grid)
self.n_steps = self.grid_steps.shape[0]
def next_path(self):
e = np.random.normal(0.0, 1.0, self.n_steps)
spot = self.process.x0()
dw = e * self.grid_steps
path = np.zeros(self.n_steps, dtype=float)
for i in range(self.n_steps):
dt = self.grid_steps[i]
t = self.time_grid[i]
spot = self.process.evolve(t, spot, dt, dw[i])
path[i] = spot
return path
class MonteCarloPricerPRDC:
def __init__(self, valuation_date, coupon_schedule, day_counter, notional, discount_curve_handle,
payoff_function, fx_path_generator, n_paths, intro_coupon_schedule, intro_coupon_rate):
self.valuation_date = valuation_date
self.coupon_schedule = coupon_schedule
self.day_counter = day_counter
self.notional = notional
self.discount_curve_handle = discount_curve_handle
self.payoff_function = payoff_function
self.fx_path_generator = fx_path_generator
self.n_paths = n_paths
self.intro_coupon_schedule = intro_coupon_schedule
self.intro_coupon_rate = intro_coupon_rate
#
self.create_coupon_dates()
def create_coupon_dates(self):
self.all_coupon_dates = np.array(self.coupon_schedule)
self.past_coupon_dates = self.all_coupon_dates[self.all_coupon_dates < self.valuation_date]
n_past_coupon_dates = self.past_coupon_dates.shape[0] - 1
self.past_coupon_rates = np.full(n_past_coupon_dates, 0.0, dtype=float)
self.remaining_coupon_dates = self.all_coupon_dates[self.all_coupon_dates > self.valuation_date]
self.time_grid = np.array([self.day_counter.yearFraction(self.valuation_date, date)
for date in self.remaining_coupon_dates])
self.grid_steps = np.concatenate((np.array([self.time_grid[0]]), np.diff(self.time_grid)))
self.n_steps = self.grid_steps.shape[0]
if(self.intro_coupon_schedule==None):
self.has_intro_coupon = False
else:
self.intro_coupon_dates = np.array(self.intro_coupon_schedule)
self.remaining_intro_coupon_dates = self.intro_coupon_dates[self.intro_coupon_dates > self.valuation_date]
self.n_remaining_intro_coupon_dates = self.remaining_intro_coupon_dates.shape[0]
if(self.n_remaining_intro_coupon_dates > 0):
self.has_intro_coupon = True
else:
self.has_intro_coupon = False
def simulate_coupon_rates(self):
self.simulated_coupon_rates = np.zeros(self.n_steps, dtype=float)
for i in range(self.n_paths):
path = self.fx_path_generator.next_path()
for j in range(self.n_steps):
self.simulated_coupon_rates[j] += self.payoff_function(path[j])
self.simulated_coupon_rates = self.simulated_coupon_rates / self.n_paths
if(self.has_intro_coupon): self.append_intro_coupon_rates()
self.coupon_rates = np.concatenate((self.past_coupon_rates, self.simulated_coupon_rates))
self.n_coupon_cash_flows = self.coupon_rates.shape[0]
def append_intro_coupon_rates(self):
for i in range(self.n_remaining_intro_coupon_dates):
self.simulated_coupon_rates[i] = self.intro_coupon_rate
def create_cash_flows(self):
self.coupon_cash_flows = np.empty(self.n_coupon_cash_flows, dtype=ql.FixedRateCoupon)
for i in range(self.n_coupon_cash_flows):
self.coupon_cash_flows[i] = ql.FixedRateCoupon(self.all_coupon_dates[i+1], self.notional,
self.coupon_rates[i], self.day_counter, self.all_coupon_dates[i], self.all_coupon_dates[i+1])
self.coupon_leg = ql.Leg(self.coupon_cash_flows)
redemption = ql.Redemption(self.notional, self.all_coupon_dates[-1])
self.redemption_leg = ql.Leg(np.array([redemption]))
def npv(self):
self.simulate_coupon_rates()
self.create_cash_flows()
self.redemption_leg_npv = ql.CashFlows.npv(self.redemption_leg, self.discount_curve_handle, False)
self.coupon_leg_npv = ql.CashFlows.npv(self.coupon_leg, self.discount_curve_handle, False)
date = [payment.date() for payment in self.coupon_leg]
amount = [payment.amount() for payment in self.coupon_leg]
amount[-1] += self.notional
pv = [ql.CashFlows.npv(np.array([payment]), self.discount_curve_handle, False) for payment in self.coupon_leg]
pv[-1] += self.redemption_leg_npv
self.cash_flow_table = np.array([date, amount, pv])
return self.coupon_leg_npv + self.redemption_leg_npv
def process_factory():
today = ql.Settings.instance().evaluationDate
domestic_curve = ql.FlatForward(today, ql.QuoteHandle(ql.SimpleQuote(0.01)), ql.Actual360())
domestic_curve = ql.YieldTermStructureHandle(domestic_curve)
foreign_curve = ql.FlatForward(today, ql.QuoteHandle(ql.SimpleQuote(0.03)), ql.Actual360())
foreign_curve = ql.YieldTermStructureHandle(foreign_curve)
fx_vol = ql.QuoteHandle(ql.SimpleQuote(0.1))
fx_vol_curve = ql.BlackVolTermStructureHandle(ql.BlackConstantVol(today, ql.NullCalendar(), fx_vol, ql.Actual360()))
fx_spot = ql.QuoteHandle(ql.SimpleQuote(133.2681))
return ql.GarmanKohlagenProcess(fx_spot, foreign_curve, domestic_curve, fx_vol_curve)
today = ql.Date(11, 4, 2023)
ql.Settings.instance().evaluationDate = today
# create discount curve
discount_curve = ql.FlatForward(today, ql.QuoteHandle(ql.SimpleQuote(0.005)), ql.Actual360())
discount_curve_handle = ql.YieldTermStructureHandle(discount_curve)
# create FX process
process = process_factory()
# create schedules for coupon- and intro coupon payments
effectiveDate = ql.Date(3, ql.September, 2015)
terminationDate = ql.Date(3, ql.September, 2041)
coupon_schedule = ql.MakeSchedule(effectiveDate, terminationDate, ql.Period(6, ql.Months),
backwards=True, calendar=ql.TARGET(), convention=ql.ModifiedFollowing)
intro_coupon_termination_date = ql.Date(3, ql.September, 2016)
intro_coupon_schedule = ql.MakeSchedule(effectiveDate, intro_coupon_termination_date, ql.Period(6, ql.Months),
backwards=True, calendar=ql.TARGET(), convention=ql.ModifiedFollowing)
# create FX path generator
fx_path_generator = PathGenerator(today, coupon_schedule, ql.Actual360(), process)
# create PRDC pricer
notional = 300000000.0
intro_coupon_rate = 0.022
n_paths = 10000
prdc_payoff_function = lambda fx_rate : min(max(0.122 * (fx_rate / 120.0) - 0.1, 0.0), 0.022)
prdc_pricer = MonteCarloPricerPRDC(ql.Settings.instance().evaluationDate, coupon_schedule, ql.Actual360(),notional,
discount_curve_handle, prdc_payoff_function, fx_path_generator, n_paths, intro_coupon_schedule, intro_coupon_rate)
# request results
npv_ccy = prdc_pricer.npv()
print('PV in CCY: {}'.format(npv_ccy))
jpy_eur = 145.3275
npv_eur = npv_ccy / jpy_eur
print('PV in EUR: {}'.format(npv_eur))
print()
print('Cash flow dates: {}'.format(prdc_pricer.cash_flow_table[0]))
print()
print('Cash flows: {}'.format(prdc_pricer.cash_flow_table[1]))
print()
print('Present values of cash flows: {}'.format(prdc_pricer.cash_flow_table[2]))