Short-term barrier option price expansion

Battle Count: 50

Highly relevant for desks trading exotic derivatives. Provides a fast, accurate approximation for pricing barrier options under stochastic and rough volatility models, which are computationally expensive to price via standard Monte Carlo or PDE methods. Useful for calibration and real-time pricing.

The analytical formulas for the correction terms are explicit but involve integrals of killed Brownian transition densities. For regular models (H=1/2), the correction is simple (based on skew). For rough models (H<1/2), it reduces to a one-dimensional integral, which is computationally efficient compared to full simulation.

The paper provides explicit formulas for the corrections and details the Monte Carlo simulation protocols (path counts, time steps, discretization schemes like 3R hybrid for rough volatility). However, it does not provide a direct link to code repositories, though the methodology is fully described.