Matrix Approximation of Bachelier Option Prices and Greeks under Stochastic Volatility models

The paper introduces a linear-algebra-based numerical method to price options and compute their sensitivities (Greeks) under Bachelier-type models with stochastic volatility. Its key feature is that it can produce prices and Greeks across many strikes at once by evaluating only a finite, fixed number of expectations, rather than recomputing for each strike. It demonstrates the approach on the SABR and rough Bergomi models, and derives an explicit convergence range for SABR.

Why it matters: Practitioners who price or hedge options — particularly in rate or spread markets where Bachelier (normal) models are used — may find this relevant for faster, more efficient computation across a strike surface. The efficiency gain could matter for calibration and risk workflows involving stochastic-volatility models like SABR or rough Bergomi.

• A single set of finitely many expectations yields prices and Greeks for many strikes within a convergence range.
• Applies to Bachelier-type (normal) models with stochastic volatility, including SABR and rough Bergomi.
• An explicit convergence range is derived for the SABR model.
• Method relies on elementary linear algebra, potentially easing implementation.

⚠ This is a computational/numerical methods paper with results valid only within a convergence range; it offers no trading signal or evidence of profitability.