feat(quantlib): add finite-difference sensitivity Greeks for barrier options

[santhreal]

Summary

Implements central finite-difference calculation of sensitivity Greeks (Delta, Gamma, Theta, Vega, Rho) for single-barrier options.

Changes

• Added barrier_greeks in agent/src/quantlib/options.py supporting all 8 standard barrier option configurations with Greek scaling consistent with bs_greeks.
• Added comprehensive unit tests in agent/tests/quantlib/test_options.py.

Signed-off-by: santhreal 64453045+santhreal@users.noreply.github.com

[he-yufeng]

This one is a real implementation and the finite differences are correct where the price is smooth. The hard case for barrier Greeks is near the barrier, and that is where this breaks: with dS = 1e-4 * S, any spot within that distance of H puts one stencil leg across the barrier, where the knock-out value collapses to the rebate, so delta and gamma come out wrong exactly where barrier Greeks matter most. The test only covers the far-from-barrier case, which is the easy one.

Could you add either a one-sided stencil when the stencil would cross H, or at minimum a documented limitation plus a near-barrier test pinning the current behavior? Happy to approve once the hard case is handled or honestly bounded.