

フナハシ ヒデハル
Funahashi Hideharu 舟橋 秀治 所属 神奈川大学 経済学部 経済学科/現代ビジネス学科 職種 准教授 

言語種別  英語 
発行・発表の年月  2017/12 
形態種別  学術雑誌 
査読  査読あり 
標題  Funahashi H and Kijima M (2017), "A Solution to the TimeScale Fractional Puzzle in the Implied Volatility," Fractal and Fractional, 1(1), 117 
執筆形態  共著 
掲載誌名  Fractal and Fractional 
掲載区分  国外 
巻・号・頁  1(1),pp.117 
著者・共著者  Hideharu Funahashi, Masaaki Kijima 
概要  In the option pricing literature, it is well known that (i) the decrease in the smile amplitude is much slower than the standard stochastic volatility models and (ii) the term structure of the atthemoney volatility skew is approximated by a powerlaw function with the exponent close to zero. These stylized facts cannot be captured by standard models, and while (i) has been explained by using a fractional volatility model with Hurst index H > 1/2, (ii) is proven to be satisfied by a rough volatility model with H < 1/2 under a riskneutral measure. This paper provides a solution to this fractional puzzle in the implied volatility. Namely, we construct a twofactor fractional volatility model and develop an approximation formula for European option prices. It is shown through numerical examples that our model can resolve the fractional puzzle, when the correlations between the underlying asset process and the factors of rough volatility and persistence belong to a certain range. 