Option pricing of fractional version of the Black-Scholes model with Hurst exponent \(H\) being in \((\frac{1}{3},\frac{1}{2})\).
The fractional Brownian motions with the Hurst exponent H have been used to replace the standard Brownian motion in the Black-Scholes' pricing model by many authors to meet the real data in the security market. The authors of the present paper announce that the used approach for the option pricing of these model is no more valid when \(H < \frac{1}{2}\) and suggest to use two risk securities and an Ito-formula-like Taylor expansion to realize hedging and obtain the pricing PDE for the European call and put in the case of \( \frac{1}{3}<H < \frac{1}{2}\).
fractional version of Black-Scholes model
scientific article; zbMATH DE number 1901673