TreeSwaptionEngine mispricing

[ralfkonrad]

Inspired by the problem in #930 I have tested the same for the TreeSwaptionEngine where we use the same snapping time mechanism as in the TreeCallableFixedRateBondEngine.

We have a similar problem here as well. The coupon date is at 2030-05-15 and when we change the call dates the next day the FdHullWhiteSwaptionEngine calculates a jump from 10.26 to 28.79 regarding. The TreeSwaptionEngine price jumps only seven days later.

Probably not that severe as in the TreeCallableFixedRateBondEngine as call dates shortly after coupon dates are not very common but I think the problem of misordered events is the same here.

Testing snap of exercise dates for discretized swaption...
Call date          FD    Tree
2030-05-06      10.11   11.04
2030-05-07      10.13   10.98
2030-05-08      10.15   10.92
2030-05-09      10.16   10.85
2030-05-10      10.18   10.78
2030-05-13      10.23   10.69
2030-05-14      10.25   10.83
2030-05-15      10.26   10.96
2030-05-16      28.79   10.92
2030-05-17      28.83   10.88
2030-05-20      28.94   10.97
2030-05-21      28.98   10.80
2030-05-22      29.01   10.69
2030-05-23      29.05   30.97
2030-05-24      29.09   30.99

    BOOST_TEST_MESSAGE("Testing snap of exercise dates for discretized swaption...");

    Date today = Date(8, Jul, 2021);
    SavedSettings backup;
    Settings::instance().evaluationDate() = today;

    RelinkableHandle<YieldTermStructure> termStructure;
    termStructure.linkTo(ext::make_shared<FlatForward>(today, 0.02, Actual365Fixed()));

    auto makeBermudanSwaption = [&today, &termStructure](Date callDate) {
        auto effectiveDate = Date(15, May, 2025);
        auto index = ext::make_shared<Euribor3M>(termStructure);
        ext::shared_ptr<VanillaSwap> swap = MakeVanillaSwap(Period(10, Years), index, 0.05)
                                                .withEffectiveDate(effectiveDate)
                                                .withNominal(10000.00)
                                                .withType(Swap::Type::Payer);

        std::vector<Date> exerciseDates{effectiveDate, callDate};
        auto bermudanExercise = ext::make_shared<BermudanExercise>(exerciseDates);
        auto bermudanSwaption = ext::make_shared<Swaption>(swap, bermudanExercise);

        return bermudanSwaption;
    };

    BOOST_TEST_MESSAGE("Call date\t   FD\t Tree");
    for (int i = -10; i < 11; i++) {
        static auto initialCallDate = Date(15, May, 2030);
        static auto calendar = Euribor3M().fixingCalendar();

        auto callDate = initialCallDate + i * Days;
        if (calendar.isBusinessDay(callDate)) {
            auto bermudanSwaption = makeBermudanSwaption(callDate);

            auto model = ext::make_shared<HullWhite>(termStructure);

            bermudanSwaption->setPricingEngine(ext::make_shared<FdHullWhiteSwaptionEngine>(model));
            auto npvFD = bermudanSwaption->NPV();

            bermudanSwaption->setPricingEngine(ext::make_shared<TreeSwaptionEngine>(model, 40));
            auto npvTree = bermudanSwaption->NPV();

            BOOST_TEST_MESSAGE(io::iso_date(callDate) << "\t" << std::fixed << std::setprecision(2)
                                                      << std::setw(5) << npvFD << "\t" << npvTree);
        }
    }

[lballabio]

Thanks, Ralf. May you also check what happens if you remove the bit of code that changes the call dates?

[ralfkonrad]

Sure!

Now TreeSwaptionEngine jumps at 2030-05-16 as well.

But we see the numerical issue why the dates are snapped. The FdHullWhiteSwaptionEngine is monotonically increasing which seems reasonable to me. But TreeSwaptionEngine isn't even one month later. I haven't played around with the timeSteps, this might help (a bit?!).

Call date          FD    Tree
2030-05-06      10.11   11.04
2030-05-07      10.13   10.98
2030-05-08      10.15   10.92
2030-05-09      10.16   10.85
2030-05-10      10.18   10.78
2030-05-13      10.23   10.69
2030-05-14      10.25   10.83
2030-05-15      10.26   10.96
2030-05-16      28.79   30.78
2030-05-17      28.83   30.78
2030-05-20      28.94   30.88
2030-05-21      28.98   30.90
2030-05-22      29.01   30.78
2030-05-23      29.05   30.97
2030-05-24      29.09   30.99
2030-05-27      29.20   31.19
2030-05-28      29.23   31.16
2030-05-29      29.27   31.05
2030-05-30      29.31   31.19
2030-05-31      29.34   31.39
2030-06-03      29.45   31.13
2030-06-04      29.49   31.27
2030-06-05      29.53   31.47
2030-06-06      29.56   31.64
2030-06-07      29.60   31.73
2030-06-10      29.71   31.47
2030-06-11      29.75   31.27
2030-06-12      29.78   31.45
2030-06-13      29.82   31.53
2030-06-14      29.86   31.70

I simply used return false here. I guess that's what you meant?

        bool withinPreviousWeek(const Date& d1, const Date& d2) {
            return false;
            // return d2 >= d1-7 && d2 <= d1;
        }

        bool withinNextWeek(const Date& d1, const Date& d2) {
            return false;
            // return d2 >= d1 && d2 <= d1 + 7;
        }

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