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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…
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.…
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…
Limit distribution of errors in discretization of stochastic Volterra equations with multidimensional kernel
Masaaki Fukasawa, Minato Hojo
This paper investigates the limit distribution of discretization errors in stochastic Volterra equations (SVEs) with general multidimensional kernel structures. While prior studies…
Backward stochastic difference equations on lattices with application to market equilibrium analysis
Masaaki Fukasawa, Takashi Sato, Jun Sekine
We study backward stochastic difference equations (BSΔE) driven by a d-dimensional stochastic process on a lattice whose increments have only d + 1 possible values that generates t…
A limit theorem for generalized tempered stable processes and their quadratic variations with stable index tending to two
Masaaki Fukasawa, Mikio Hirokane
We study the limit of the joint distribution of a multidimensional Generalized Tempered Stable (GTS) process and its quadratic covariation process when the stable index tends to tw…