Models with Transaction Cost for Pricing European Options and Hedging

Abstract

In this paper models with transaction costs for pricing of European options using mixed fractional Brownian motion (fbm) and Partial differential equation (PDE) model are considered. Investigation on price sensitivity to volatility and formulation of asymptotic strategy for replicating self financing assets are also made. Simulation experiments for the models are run to obtain the call and put prices using fbm with Hurst parameter and the Crank-Nicolson method for the numerical solution to the PDE model. It is found that stock prices increase with time to maturity dates, whereas, the call prices decrease steadily as time approaches maturity dates in conformity with theta hedging strategy.