انتخاب روش قیمت گذاری اروپا با هزینه های معاملات تحت حافظه بلند مدل نوسانات تصادفی جزء به جزء

This paper deals with the problem of discrete time option pricing using the fractional long memory stochastic volatility model with transaction costs. Through the ‘anchoring and adjustment’ argument in a discrete time setting, a European call option pricing formula is obtained.

Over the last few years, the financial markets are regarded as complex and nonlinear dynamic systems. A series of studies have found that many financial market time series display scaling laws and that there exist the excess kurtosis and skewness in the stock price returns. It is also well known that the returns and the volatilities of the stock prices often exhibit the long memory property where the autocorrelation of the returns and the absolute and squared returns of time series are characterized by a very slow decay. These features are the crucial components of asset risk management, investment portfolios and option pricing, for their presences are closely connected to the predictability of the return and volatility. Therefore, it has been proposed that one should replace the Brownian motions in the classical Black–Scholes model [1] and the Hull–White stochastic volatility model [2] by two processes with long-range dependence. A simple modification, named the fractional long memory stochastic volatility model, is to introduce fractional Brownian motion (fBm) as the source of randomness. Thus, one adds two parameters, HH and H1H1, in the Hull–White-like stochastic volatility model, to model the dependence structures in the stock returns and the volatilities. The fractional long memory stochastic volatility model can capture the excess kurtosis and skewness of the stock price returns and the long-range dependence in the stock returns and volatilities.

In this paper, on the basis of the points of view of behavioral finance and econophysics and empirical findings of the long-range dependence in stock returns, we obtain a European call option pricing formula with transaction costs for the fractional long memory stochastic volatility model with Hurst exponent View the MathML sourceH∈[12,1). It has been shown that the anchoring-adjustment behavior of investors and the reference point effect play an important role in option pricing with Hurst exponent View the MathML sourceH∈[12,1) and the decision process influences decision outcome. In particular, option pricing is strongly influenced by the time scaling δtδt and Hurst exponent HH