Add IFT + AAD sensitivity for SANOS LP calibration

[mar20tinha-dot]

Summary

Compute exact sensitivities of any downstream exotic price w.r.t. all vanilla option quotes — through the SANOS LP calibration — without re-calibrating.

Part I: IFT through LP (pure Python)

At the LP optimum, active constraints define an invertible linear system. The Implicit Function Theorem gives the exact Jacobian ∂C_fit/∂quote from a single linear solve.

Part II: AAD downstream (C++/AADC)

The MC pricing kernel (surface → local vol → GBM → barrier payoff) is recorded on an AADC tape. One reverse pass gives ∂price/∂surface for all grid nodes.

Chain rule

∂V/∂quote = (∂V/∂surface) × (∂surface/∂quote)
              AAD (C++)        IFT (Python)

All N sensitivities from 1 LP + 1 linear solve + 1 AAD MC pass.

Files added

File	Description
cvxpy_ift.py	Reusable IFT module for any LP (scipy.linprog)
example_sanos_ift.py	Self-contained: calibrate + IFT + validate + benchmark
sanos_full_test.py	Multi-expiry LP + IFT + downstream (pure Python)
sanos_downstream_aadc.cpp	Barrier MC with AADC reverse-mode AD
sanos_e2e_test.py	End-to-end: Python IFT + C++ AAD + chain rule
README_ift.md	Full documentation

Benchmarks

Setup	Bump	IFT+AAD	Speedup
15 quotes, IFT only	38 ms	1.6 ms	24×
33 quotes, IFT only	340 ms	8.5 ms	40×
33 quotes, end-to-end	602 s	9.1 s	66×

Dependencies

• Part I: numpy, scipy (no additional deps)
• Part II: AADC by MatLogica (optional — Part I works standalone)

References

1. Goloubentsev, Lakshtanov, Piterbarg (2022). "Automatic Implicit Function Theorem." Risk, March 2022. SSRN 3984964
2. Dupire (1994). "Pricing with a smile." Risk, 7(1), 18-20.