The skew Brownian motion should not be used as a risk-neutral returns process: a well-posed skew-normal alternative

Battle Count: 102

Highly relevant for quantitative finance practitioners working on derivatives pricing, model validation, and risk management. The paper corrects fundamental errors in a popular class of option pricing models (GSBM), which directly impacts trading strategies based on these models. The SNLV model provides a well-posed alternative for skew modeling. However, it is primarily a theoretical correction paper rather than a trading strategy paper. Practitioners using GSBM-based models need to reassess their implementations.

The theoretical framework requires deep knowledge of stochastic analysis (local times, SDEs, martingale theory, arbitrage theory). The SNLV model itself has closed-form option prices and a computable local volatility function, making numerical implementation feasible. However, the singularity at the origin in the local volatility surface requires careful numerical treatment. The arbitrage strategies are theoretically simple (one-touch strategies on local time support) but practically difficult to implement.

The paper is fully theoretical with all proofs provided in the main text and appendices. All formulae are explicitly derived. Numerical illustrations (Figures 1-5) use specific parameter values (S0=100, σ=0.5, δ=-0.6, r=0) that can be reproduced. However, no code repository is provided. The mathematical derivations are self-contained and verifiable.