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European cash-or-nothing options

The additive factory exposes the existing cash-or-nothing payoff through the ordinary option facades in Python and C/Go. Existing vanilla constructors and signatures are unchanged.

Language Constructor Analytic engine
Python VanillaOption.cash_or_nothing(option_type, strike, cash_payoff, expiry, settings) option.set_engine(process) or option.price(process)
Go session.NewCashOrNothingOption(kind, strike, cashPayoff, expiry, settings) option.SetEngine(process) or option.Price(process)
C itofin_option_cash_or_nothing_new Existing itofin_option_set_engine, engine kind0

Supported scope

  • European exercise and a fixed cash amount. The raw payoff pays cash for a call strictly above strike or a put strictly below strike; otherwise it pays zero.
  • The analytic European Black-Scholes engine, using the process's existing discount, dividend and volatility inputs. Values and ordinary Greeks reuse the existing option query methods and the original core implementation.
  • Strike must be finite and nonnegative. Cash must be finite; signed and zero cash are accepted. Cash is a currency amount, not a probability or notional multiplier.
  • The constructor retains settings. An attached engine retains its process and live curves/quotes, so releasing input wrappers does not destroy the option's dependencies. Evaluation-date and observable market changes invalidate pricing.
  • C uses the existing typed, thread-confined context handles, writes the constructor output only on success, and requires callers to satisfy the C pointer contract. Go rejects foreign-session inputs and serializes native calls on its worker. Python retains its existing unsendable native ownership.

Numerical and engine limits

This is a binding, not a repair to digital-option mathematics or a claim of full QuantLib parity. Existing core behavior, including errors, is retained.

  • At zero or sub-epsilon standard deviation, digital price uses the original deterministic/ATM-half branch. The delta/rho ladder is inherited from the core's plain-vanilla-style fallback, including for zero cash. These are not textbook digital Greek limits. In particular, put delta, risk-free rho and dividend rho differ from the independent compiled QuantLib 1.43 reference on the zero/sub-epsilon diagnostic grid. The raw payoff's strict strike comparison is distinct from the analytic zero-volatility convention.
  • Non-notifying settings retain the ordinary option's cached-versus-fresh behavior. At evaluation date equal to expiry, changing include_reference_date_events after calculating can leave the cached value at zero while a freshly constructed plain/digital option has nonzero value. This also occurs in the native reference. Reconstructing the option or reattaching its engine restores the fresh result. This factory adds neither silent-policy synchronization nor new freeze/unfreeze methods.
  • Zero strike and extreme market inputs retain the existing calculator's singular/nonfinite-result behavior. At zero strike, gamma, theta and vega can return NaN for both calls and puts, as in the independent native diagnostic. Constructibility does not guarantee finite Greeks or convert those inherited nonfinite results into exceptions.
  • Analytic Heston, Merton, Bates and analytic GJR engines require a plain-vanilla payoff and reject this digital payoff through their existing core checks. Other generic MC/FD engine paths are not certified by this factory. No new engine compatibility, payoff visitor or numerical algorithm is introduced.
  • Asset-or-nothing, gap and percentage-strike payoff factories, American digital exercise and the wider payoff family remain outside this slice.

Examples

Python: cash digital example. Go: cash digital example.

Fixtures compare regular positive-volatility prices and Greeks to an independent normal-distribution formula, while boundary regressions explicitly pin original core behavior. Retained-input, date/quote invalidation and native-error probes are separate from those numerical checks. Source contract: existing crates/libitofin/src/instruments/payoffs.rs, pricingengines/blackcalculator.rs and pricingengines/vanilla/mod.rs.

Validation qualifications

Ordinary positive-volatility closed-form checks are separate from the known boundary diagnostics. Original-artifact public clients passed 392 Python and 442 C checks, including 140 ordinary closed-form price/Greek fields per facade.

The separate strict native-edge diagnostic exited 1 and retained 27 distinct finite put-Greek differences, 54 when counted across the C and Python facades. Its grid used volatility 0, 1e-18 and 1e-16, strikes 80/100/120, and a one-year horizon. The six distinct zero-strike call/put gamma/theta/vega routes were nonfinite in both facades and the reference, not successful finite-Greek comparisons. Of 210 shared C/Python edge routes, 204 were finite and bit-identical and six had matching nonfinite classifications. Facade equivalence is not native numerical parity.

The separate strict silent-policy diagnostic exited 1 in each facade: cached plain/digital values 0 differed from fresh 20/17; engine reattachment restored 20/17. This matched the independent native reference and is retained, not repaired or hidden by a tolerance change. The compiled QuantLib 1.43 package is a separately qualified reference, not a binary claimed to come from the local 1.43-dev checkout.