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math.PR2026
Short-maturity skew stickiness ratio under local volatility
Masaaki Fukasawa
We prove that the skew stickiness ratio converges to two at short maturity under local volatility models. This appears to be the first rigorous proof of this limit for a general ti…
math.PR2026
Error Distribution of the Local Linearization Method for Stochastic Differential Equations with Additive Brownian Noise
Masaaki Fukasawa, Mikio Hirokane, Kostas Kardaras
We prove a functional stable limit theorem for the discretization error process of a local linearization scheme for stochastic differential equations with additive Brownian noise.…
math.PR2026
Martingale expansion for stochastic volatility
Masaaki Fukasawa
The martingale expansion provides a refined approximation to the marginal distributions of martingales beyond the normal approximation implied by the martingale central limit theor…