Innovative Extensions to Option Pricing: Asymmetric Brownian Motion and Random Walk Approaches

Battle Count: 50

Highly relevant for derivatives pricing desks, volatility trading, and risk management. The GABM framework provides a theoretically grounded alternative to jump-diffusion and stochastic volatility models for capturing skewness and state-dependent volatility in option markets. The binomial tree implementation enables practical pricing and hedging. The implied volatility surface calibration methodology is directly applicable to market-making and volatility arbitrage strategies. However, the path-dependence and mathematical complexity may limit real-time implementation without significant engineering effort.

The theoretical framework requires advanced knowledge of stochastic calculus, local time theory, and invariance principles. The binomial tree construction is moderately complex due to state-dependent volatility at each node. Monte Carlo simulation of sign paths on the recombining lattice is computationally feasible but requires careful handling of the NIG density evaluation at each node. The calibration pipeline (PCHIP interpolation, Gaussian kernel smoothing, no-arbitrage constraints) adds engineering complexity. The closed-form PDE solution requires numerical methods due to path-dependence on B_t.

The paper provides detailed mathematical derivations, explicit formulas for GABM dynamics, binomial tree construction, and calibration procedures. However, no code repository is mentioned. Empirical data is sourced from Bloomberg Professional Services, which is proprietary. Parameter values (Table 1) and calibration methodology are described, but full implementation details for the Monte Carlo simulation and PCHIP interpolation are partially specified. The theoretical framework is rigorous and reproducible for those with stochastic calculus expertise.