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"""
Copyright (C) 2025 Hiroto Ogawa
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it
under the terms of the QuantLib license. You should have received a
copy of the license along with this program; if not, please email
<quantlib-dev@lists.sf.net>. The license is also available online at
<https://www.quantlib.org/license.shtml>.
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the license for more details.
"""
import unittest
import math
import QuantLib as ql
LAG = 0
DC = ql.ActualActual(ql.ActualActual.ISDA)
CAL = ql.NullCalendar()
def flat_rate(rate):
return ql.FlatForward(
LAG, CAL, ql.makeQuoteHandle(rate), DC)
class PerpetualFuturesTest(unittest.TestCase):
def test_perpetual_futures(self):
""" Testing PerpetualFutures pricing by discounted cashflow method against analytic formulae. """
val_date = ql.Date(20, 6, 2025)
ql.Settings.instance().evaluationDate = val_date
test_dicts = [
# Discrete time
{"payoff": ql.PerpetualFutures.Linear, "funding": ql.PerpetualFutures.FundingWithPreviousSpot,
"freq": ql.Period(3, ql.Months), "spot": 10000., "domRate": 0.04, "btcYield": 0.02,
"fundingRate": 0.01, "rateDiff": 0.005, "tol": 1.e-6},
{"payoff": ql.PerpetualFutures.Linear, "funding": ql.PerpetualFutures.FundingWithCurrentSpot,
"freq": ql.Period(3, ql.Months), "spot": 10000., "domRate": 0.04, "btcYield": 0.02,
"fundingRate": 0.01, "rateDiff": 0.005, "tol": 1.e-6},
{"payoff": ql.PerpetualFutures.Inverse, "funding": ql.PerpetualFutures.FundingWithPreviousSpot,
"freq": ql.Period(3, ql.Months), "spot": 10000., "domRate": 0.04, "btcYield": 0.02,
"fundingRate": 0.01, "rateDiff": 0.005, "tol": 1.e-6},
{"payoff": ql.PerpetualFutures.Inverse, "funding": ql.PerpetualFutures.FundingWithCurrentSpot,
"freq": ql.Period(3, ql.Months), "spot": 10000., "domRate": 0.04, "btcYield": 0.02,
"fundingRate": 0.01, "rateDiff": 0.005, "tol": 1.e-6},
# Continuous time
{"payoff": ql.PerpetualFutures.Linear, "funding": ql.PerpetualFutures.FundingWithPreviousSpot,
"freq": ql.Period(0, ql.Months), "spot": 10000., "domRate": 0.04, "btcYield": 0.02,
"fundingRate": 0.2, "rateDiff": 0.005, "tol": 1.e-6},
{"payoff": ql.PerpetualFutures.Inverse, "funding": ql.PerpetualFutures.FundingWithPreviousSpot,
"freq": ql.Period(0, ql.Months), "spot": 10000., "domRate": 0.04, "btcYield": 0.02,
"fundingRate": 0.2, "rateDiff": 0.005, "tol": 1.e-6},
]
for d in test_dicts:
pf = ql.PerpetualFutures(d["payoff"], d["funding"], d["freq"], CAL, DC)
domYC = ql.YieldTermStructureHandle(flat_rate(d["domRate"]))
btcYC = ql.YieldTermStructureHandle(flat_rate(d["btcYield"]))
spot = ql.QuoteHandle(ql.SimpleQuote(d["spot"]))
fundingTimes = [0.0]
fundingRates = [d["fundingRate"]]
ir_diffs = [d["rateDiff"]]
engine = ql.DiscountingPerpetualFuturesEngine(domYC, btcYC, spot, fundingTimes, fundingRates, ir_diffs,
ql.DiscountingPerpetualFuturesEngine.PiecewiseConstant)
# pricing
pf.setPricingEngine(engine)
npv = pf.NPV()
# analytic price
# for details, refer to
# Perpetual Futures Pricing, Damien Ackerer, Julien Hugonnier, Urban Jermann, 2024
# https://finance.wharton.upenn.edu/~jermann/AHJ-main-10.pdf
period = d["freq"]
length = float(period.length())
unit = period.units()
if unit == ql.Years:
dt = length
elif unit == ql.Months:
dt = length / 12.
elif unit == ql.Weeks:
dt = length * 7. / 365.
elif unit == ql.Days:
dt = length / 365.
elif unit == ql.Hours:
dt = length / 365. / 24.
elif unit == ql.Minutes:
dt = length / 365. / 24. / 60.
elif unit == ql.Seconds:
dt = length / 365. / 24. / 60. / 60.
else:
raise RuntimeError("unknown funding frequency unit: " + str(unit))
# Discrete time
if length > 0:
if d["payoff"] == ql.PerpetualFutures.Linear:
if d["funding"] == ql.PerpetualFutures.FundingWithPreviousSpot:
# Equation (12) in the above paper
expected = (
d["spot"] * (d["fundingRate"] - d["rateDiff"]) * math.exp(d["btcYield"] * dt) /
(math.exp(d["btcYield"] * dt) - math.exp(d["domRate"] * dt) + d["fundingRate"] * math.exp(d["btcYield"] * dt)))
elif d["funding"] == ql.PerpetualFutures.FundingWithCurrentSpot:
# at the end of "3 Perpetual futures pricing" in the above paper
expected = (
d["spot"] * (d["fundingRate"] - d["rateDiff"]) * math.exp(d["domRate"] * dt) /
(math.exp(d["btcYield"] * dt) - math.exp(d["domRate"] * dt) + d["fundingRate"] * math.exp(d["domRate"] * dt)))
elif d["payoff"] == ql.PerpetualFutures.Inverse:
if d["funding"] == ql.PerpetualFutures.FundingWithPreviousSpot:
# "Proposition 2" in the above paper
expected = (
d["spot"] *
(math.exp(d["domRate"] * dt) - math.exp(d["btcYield"] * dt) + d["fundingRate"] * math.exp(d["domRate"] * dt)) /
(d["fundingRate"] - d["rateDiff"]) / math.exp(d["domRate"] * dt))
elif d["funding"] == ql.PerpetualFutures.FundingWithCurrentSpot:
expected = (
d["spot"] *
(math.exp(d["domRate"] * dt) - math.exp(d["btcYield"] * dt) + d["fundingRate"] * math.exp(d["btcYield"] * dt)) /
(d["fundingRate"] - d["rateDiff"]) / math.exp(d["btcYield"] * dt))
else:
# Continuous time
if d["payoff"] == ql.PerpetualFutures.Linear:
# "Proposition 3" in the above paper
expected = d["spot"] * (d["fundingRate"] - d["rateDiff"]) / (d["btcYield"] - d["domRate"] + d["fundingRate"])
elif d["payoff"] == ql.PerpetualFutures.Inverse:
# "Proposition 4" in the above paper
expected = d["spot"] * (d["domRate"] - d["btcYield"] + d["fundingRate"]) / (d["fundingRate"] - d["rateDiff"])
failed_msg = f"Perpetual future price {npv} differs from analytic price {expected} with relative tolerance {d['tol']}\n"
self.assertAlmostEqual(npv, expected, delta=d["tol"] * expected, msg=failed_msg)
if __name__ == '__main__':
print("testing QuantLib", ql.__version__)
unittest.main(verbosity=2)
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