Analytic approximation for Bachelier option prices and applications

Battle Count: 75

Highly relevant for quantitative traders dealing with interest rate options, commodity options, or any market where the Bachelier (normal) model applies. The analytical expansion enables fast pricing and Greeks computation, critical for real-time trading. The Monte Carlo variance reduction technique is directly applicable to risk management and pricing engines. However, the paper is primarily theoretical/mathematical rather than strategy-focused.

The core expansion (Theorem 3.4) requires computing negative non-integer moments of the integrated variance M_T, which can be done via Monte Carlo or analytically for specific models (Heston, SABR). The Taylor series in moneyness is straightforward to implement. Computing Greeks analytically (Remark 3.6) adds moderate complexity. The control variate application requires simulating the uncorrelated model separately. Overall, moderate implementation effort with clear mathematical formulas provided.

The paper provides explicit formulas (Theorem 3.4, Corollary 3.2, Proposition 3.1), specific parameter values for Heston and SABR models, and clear numerical procedures. However, no code repository is mentioned. The mathematical derivations are complete and self-contained, enabling reproduction of analytical results. Monte Carlo benchmarks with 100,000 simulations and antithetic variables are specified.