Double no-touch series truncation produces prices outside the cash-payment bounds

[kadyrbekovhamit-cyber]

FXDoubleOneTouchOption.value can price a nonnegative double-touch payoff below zero and its complementary no-touch payoff above the discounted cash payment. Tested through the real Numba-backed public API on source 2b9227fea9d832c4033421d6cd53a54316414fca and PyPI 1.1.2. The current master target file still matches the tested bytes when fetched today.

from financepy.products.fx.fx_double_one_touch_option import FXDoubleOneTouchOption
from financepy.utils.date import Date
from financepy.utils.global_types import DoubleBarrierTypes
from financepy.utils.day_count import DayCountTypes
from financepy.utils.frequency import FrequencyTypes
from financepy.market.curves.discount_curve_flat import DiscountCurveFlat
from financepy.models.black_scholes import BlackScholes

vdt = Date(1, 1, 2026)
expiry = vdt.add_days(30)
sigma = 0.2
d = DiscountCurveFlat(vdt, 0.5*sigma*sigma,
                      FrequencyTypes.CONTINUOUS, DayCountTypes.ACT_365F)
f = DiscountCurveFlat(vdt, 0.0,
                      FrequencyTypes.CONTINUOUS, DayCountTypes.ACT_365F)
for kind in DoubleBarrierTypes:
    price = FXDoubleOneTouchOption(expiry, kind, 80., 125., 1.).value(
        vdt, 100., d, f, BlackScholes(sigma))
    print(kind.name, price)
print("discounted cash", d.df(expiry))
# KNOCK_IN  -0.17335157473444152
# KNOCK_OUT  1.1717090894757467
# discounted cash 0.9983575147413052

Both prices must be in [0, discounted cash]. Their sum is correct even in the failing implementation, so complement parity alone misses the defect. An independent Brownian absorbing-density method-of-images calculation gives no-touch 0.9981587590142639 and touch 0.00019875572704133946.

Two truncation mistakes in _fast_double_no_touch_pricer contribute:

1. Stopping when one series term is small is not a tail bound. At zero log drift the even coefficients vanish while later odd terms can remain material. A midpoint spot also makes even sine factors vanish.
2. The stated damping bound requires n >= Z/(pi*sigma) * sqrt(2*log(1/eps)/T). The current expression is half that threshold.

Across 480 fixed parameter scenarios (two prices each), oracle failures are 360 original, 48 after removing only the early stop, 0 after both corrections, and 360 after restoring the original source. The release reproduces the original rows. Probability-range failures are 72 / 24 / 0. All 48 nonzero-drift controls and all 120 previously passing scenarios remain within the same normalized tolerance 2e-10; they are not byte-identical. All 230 original source files are preserved.

The independent oracle uses 60-decimal method-of-images arithmetic, with an image-tail check recorded in the attachment. No clipping or tolerance relaxation is used. The existing 50-term minimum and 2000-term cap remain, so the candidate does not guarantee convergence for all inputs. Full upstream suite, Monte Carlo, Greeks, performance and production impact were not measured.

The attached packet contains the candidate patch, real API probe, raw original/intermediate/candidate/restored/release results and provenance. Its scripts retain local source paths and require adapting to a checkout; it is not a standalone build distribution. SHA-256: cb52bb4189635aada44413d2222e7b4c38fa07fbf8ddfadc976d8862d9a30cdd. Bounded duplicate search refreshed today; no exact match identified.

I would be glad to prepare a focused PR and discuss a suitable convergence contract. Xamit Kadirbekov / GERO, kadyrbekovhamit@gmail.com. AI-assisted preparation; claims are tied to the retained executed evidence.

financepy-double-no-touch-triage-maintainer-evidence.zip

[domokane]

Confirmed — I can reproduce this issue.

The negative double-touch value / no-touch value above discounted cash is clearly invalid, so I'm treating this as a FinancePy bug.

I'll add the case as a regression test. If you'd like to submit the proposed truncation/convergence fix as a focused PR, please do. In particular, I'd like the PR to include tests covering the pricing bounds and touch/no-touch parity.

Thanks for the detailed reproducer and analysis.

[kadyrbekovhamit-cyber]

Thanks, @domokane. The focused fix is in #270, including the requested bounds and touch/no-touch parity tests. The exact PR plus 14 adjacent FX tests passed locally: 103 tests.

I have also published a standalone reproduction package, replacing the machine-specific paths in the original attachment:

• Permanent archive: https://doi.org/10.5281/zenodo.22805090
• Report and runnable evidence: https://github.com/kadyrbekovhamit-cyber/gero-numerical-observatory/blob/main/catalog/reports/financepy-double-no-touch-series-truncation.md

The clean replay against master 4c7cd50bdadd6efc9ac74fa81e93374397d18e3e reproduces 360 / 0 / 360 discrepant scenarios out of 480 for original / candidate / restored code. PyPI 1.1.2 reproduces the original failures. The package includes pinned source, an independent method-of-images reference, raw results and the two partial/full patch comparisons.

This is the archival release of this issue, not another bug report. The existing 2,000-term cap remains; I am not claiming convergence for every regime or production-loss measurements. Happy to adapt the patch or tests to your preferred convergence contract.