European Lookback option pricing with floating strike price under fractional Black-Scholes models

One of the most famous path-dependent options is the Lookback option. This option is a useful financial instrument to hedge against the risks associated with high volatility in the market. Since empirical studies on the statistical properties of logarithmic returns show the dependence of returns and stock price volatilities on different days; we need a suitable model for pricing the Lookback option to illustrate this phenomenon. Partial differential equations with fractional order derivatives can be useful tools to describe the long memory effect in the financial markets. Hence, we want to price the European floating strike Lookback option (FSLO) under fractional Black-Scholes (FBS) models using a numerical method: implicit difference scheme (IDS). Also, the stability and convergence analysis of the proposed method are investigated using Fourier series expansion. Numerical results are provided to show the efficiency of the method.

کلیدواژه ها:

Fractional Black-Scholes Equation ، Lookback option ، Path-dependent option ، Implicit difference scheme