Unbiased Monte Carlo Greeks for Discontinuous Payoffs

Battle Count: 73

Highly relevant for any quantitative trading desk dealing with structured products, barrier options, autocallables, or digital options. Greeks (delta, vega, rho) are fundamental for hedging and risk management. The method eliminates the need for per-product smoothing calibration, reduces model risk, and dramatically improves computational efficiency (8K paths vs 12M paths for 2% accuracy on barriers). Directly applicable to derivatives pricing, hedging, and regulatory capital calculations. The automatic nature via AADC means quant developers can integrate it into existing pricing code with minimal changes.

The mathematical derivation is sophisticated (Leibniz rule, implicit function theorem, orthogonal change of variables in Gaussian space), but the implementation is simplified by the AADC library which handles tape recording, discontinuity tracking, and replay automatically. The quant writes standard pricing code and the correction driver handles discontinuities. For simple models (GBM/LMM), only 2 kernel replays per indicator are needed. For stochastic volatility models, Newton root-finding and reverse-mode AD add complexity. The screening step (70-80% skip rate) keeps computational overhead manageable. Requires understanding of the AADC API and the correction driver interface.

Code is available on GitHub (https://github.com/lakshtanov/aadc-correction) with tests and examples. Uses open-source QuantLib models and the AADC library (pip install aadc, free for non-commercial use). Benchmarks use standard QuantLib processes (BlackScholesProcess, HestonProcess, Hull-White). However, AADC is free only for non-commercial use, which may limit industrial reproducibility. The mathematical derivation is fully self-contained with proofs.