Portal de Periódicos da CAPES

Asymptotic Behavior of the Fractional Heston Model

2018; Society for Industrial and Applied Mathematics; Volume: 9; Issue: 3 Linguagem: Inglês

10.1137/17m1142892

1945-497X

Hamza Guennoun, Antoine Jacquier, Patrick Roome, Fangwei Shi,

Complex Systems and Time Series Analysis

We consider the fractional Heston model originally proposed by Comte, Coutin, and Renault [Ann. Finance, 8 (2012), pp. 337--378]. Inspired by recent groundbreaking work on rough volatility [E. Alòs, J. León, and J. Vives, Finance Stoch., 11 (2007), pp. 571--589; C. Bayer, P. K. Friz, and J. Gatheral, Quant. Finance, 16 (2016), pp. 887--904; M. Fukasawa, Finance Stoch., 15 (2011), pp. 635--654; J. Gatheral, T. Jaisson, and M. Rosenbaum, Quant. Finance, to appear], which showed that models with volatility driven by fractional Brownian motion with short memory allow for better calibration of the volatility surface and more robust estimation of time series of historical volatility, we provide a characterization of the short- and long-maturity asymptotics of the implied volatility smile. Our analysis reveals that the short-memory property precisely provides a jump-type behavior of the smile for short maturities, thereby fixing the well-known standard inability of classical stochastic volatility models to fit the short-end of the volatility smile.