Option pricing of a bi-fractional Black–Merton–Scholes model with the Hurst exponent in

✍ Scribed by Jin-Rong Liang; Jun Wang; Wen-Jun Zhang; Wei-Yuan Qiu; Fu-Yao Ren

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 247 KB
• Volume: 23
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/j.aml.2010.03.022

✦ Synopsis

A model for option pricing of a (γ , 2H)-fractional Black-Merton-Scholes equation driven by the dynamics of a stock price S(t) satisfying (dS

, where B H (t) is a fractional Brownian motion with Hurst exponent H ∈ (0, 1), is established. We obtain the explicit option pricing formulas for the European call option and put option for γ > 0, 1 2 ≤ H ≤ 1.