Approximation Method of Pricing American-Style Asian Option in Fractional Black-Scholes Model

For deriving the approximate formula of American-style Asian option in the fractional Black-Scholes model, this paper take the American-style Asian put Option as example. First, derived the formulas of European-style geometric average Asian option with fix strike price by partial differential equation method briefly. Based on the formulas, the quadratic approximation in the standard Black-Scholes model is applied to pricing American-style geometric average Asian option with fix strike price and obtained approximate formulas. Finally, derived approximate formulas by quadratic approximation from another perspective and obtain the same result.