""" 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 . The license is also available online at . 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)