Add analytical delta to existing EquityPowerOption (positive powers only)

[AIM-IT4]

Scope of the revised PR

FinancePy already implements power-option pricing in financepy/models/bs_power_option.py and EquityPowerOption. The original draft inadvertently replaced that existing API; that has been corrected. No duplicate pricer or replacement API remains.

New functionality: a JIT-compiled analytical spot delta for European power calls and puts, exposed through the existing EquityPowerOption.delta() method. Previously the inherited EquityOption.delta() used stock-price finite differences. The new closed-form derivative is phi * n * M_n / S * N(phi*d1) for n > 0, where M_n is the discounted n-th stock-price moment already used by the existing pricing function.

Response to maintainer feedback

• Only strictly positive powers. Constructor rejects zero, negative, or non-finite power with FinError; the low-level model preserves FinancePy's existing NaN convention for non-positive powers.
• Existing pricing preserved. Restored the upstream power_option_value(s,t,k,r,q,v,opt_type_value,n) function and its signature; existing equity product valuation and Monte Carlo pricing remain unchanged.
• Precise added value. power_option_delta() in the existing model module, a product-level delta override, and a focused regression suite. No new PowerOption facade.

Verification

The new unit suite tests finite-difference agreement with the existing power-option pricer for fractional/integer positive powers, calls/puts, the n=1 Black–Scholes delta limit, quantity scaling, invalid powers and zero volatility. Finite-difference tolerances account for FinancePy's existing six-decimal approximate normcdf. 10 independent numerical formula checks passed; full repository unit/regression workflows are running on GitHub.

Related to #12 (analytical Greek enhancement to the existing product; no new FX product).

[domokane]

What is new here ? I don't want to allow negative and zero powers.

[AIM-IT4]

Thanks for pointing this out. You are right: FinancePy already has power_option_value and EquityPowerOption, and the initial PR duplicated/replaced the existing implementation. I missed that.

I've revised this PR to preserve the existing pricing API and add only an analytical spot delta to the existing power-option model and EquityPowerOption.delta(). The current base-class delta is finite-difference based, so the new contribution is the closed-form Greek and its regression coverage.

I've also removed support for non-positive powers: EquityPowerOption now rejects n <= 0 (and non-finite values). Tests cover positive fractional/integer powers, both option types, the n=1 Black–Scholes limit, and comparisons against the existing pricer. Independent numerical checks pass; the updated GitHub CI is running.

Apologies for the duplicate implementation in the initial draft. Please let me know if analytical delta is a useful addition here, or if you'd prefer a different scope.

[domokane]

Thanks!