- Date : 23 Jan. (Thu.)
- Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
- Time : 16:30 – 18:45
- Speaker 1: Ryoji Takano (Osaka University) 16:30 –17:30
- Title:On Some new integration by parts formula for finance and their Monte Carlo simulation
- Abstract:
A rough volatility model is a stochastic volatility model for an asset price process with volatility being rough, meaning that the H\”{o}lder regularity of the volatility path is less than half. In this talk, we will focus on the asymptotic behavior of the implied volatility for the short maturity and show that the short-time large deviation principle for rough volatility models characterize the asymptotic behavior of the implied volatility.
- Speaker 2:Yushi Hamaguchi (Kyoto University) 17:45 –18:45
- Title: A generalized coupling approach for the weak approximation of stochastic functional differential equations
- Abstract:
In this talk, we study functional type weak approximation of weak solutions of stochastic functional differential equations by means of the Euler–Maruyama scheme. Under mild assumptions on the coefficients, we provide a quantitative error estimate for the weak approximation in terms of the Lévy–Prokhorov metric of probability laws on the path space. The weak error estimate obtained in this paper is sharp in the topological and quantitative senses in some special cases. We apply our main result to ten concrete examples appearing in a wide range of science and obtain a weak error estimate for each model. The proof of the main result is based on the so-called generalized coupling of probability measures. This talk is based on a joint work with Dai Taguchi (Kansai University). The preprint is available at arXiv:2412.18523.
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