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 Time-Scale Fractional Puzzle in the Implied Volatility," Fractal and Fractional, 1(1), 1-17
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.1-17
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 at-the-money volatility skew is approximated by a power-law 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 risk-neutral measure. This paper provides a solution to this fractional puzzle in the implied volatility. Namely, we construct a two-factor 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.