2023/06/23 by Akihiko Takahashi, Takahashi, Akihiko, Toshihiro Yamada +1
Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Mathematical functions and polynomials #Financial Risk and Volatility Modeling
paper · pdf · doi:10.48550/arxiv.2306.13405
This paper presents a novel generic asymptotic expansion formula of expectations of multidimensional Wiener functionals through a Malliavin calculus technique. The uniform estimate of the asymptotic expansion is shown under a weaker condition on the Malliavin covariance matrix of the target Wiener functional. In particular, the method provides a tractable expansion for the expectation of an irregular functional of the solution to a multidimensional rough differential equation driven by fractional Brownian motion with Hurst index H<1/2, without using complicated fractional integral calculus for the singular kernel. In a numerical experiment, our expansion shows a much better approximation for a probability distribution function than its normal approximation, which demonstrates the validity of the proposed method.