Risk preference, option pricing and portfolio hedging with proportional transaction costs

This paper is concerned in the option pricing and portfolio hedging in a discrete time case with the proportional transaction costs. Through the Monte Carlo simulations it has been shown that the fractal scaling and risk preference of traders have an important influence on the hedging performances in both option pricing and portfolio hedging in a discrete time case. In addition, the relation between preference of traders and implied volatility frown is discussed. We conclude that the risk preferences of traders play an important role in determining the shape of the implied-volatility-frown and the different options having the different hedging frequencies is another reason for the implied volatility frown.