Survey on fractional Black-scholes with hurst exponent on European option with transaction cost

Subject Areas : Financial engineering

Morteza  Rahmani ¹ (Associate professor of mathematics university of science & culture.)
Nahid  Jafarian ² (Master student, Financial mathematic, university of science & culture)

Received: 2017-01-27 Accepted : 2017-04-30 Published : 2017-09-23

Keywords: Variational Iteration Method, Fractional Brownian motion, Fractional Black-Scholes model, Hurst exponent, European option, option valution, Transaction costs,

Abstract :

On all stock exchange of the world famous considerably derivatives are traded. Options are a patent for its owner, the most important are derivatives. The best economic tool management risk, the use of the option contract. It is obvious that at the conclusion of each contract, determining the price is the main element, Thus providing fair prices for securities is very important. In this study, the option pricing under fractional Black-Scholes is survived. The fractional Black-Scholes is based on fractional Brownian motion with hurst parameter. The Hurst exponent be associated with fractal dimension and self-similary as an indicator of long-term memory is used in the process of stock prices. The aim to provide a pricing formula for European options with transaction costs is an approximate answer fractional pricing equation with transaction costs by way of variational iteration method is checked. The transaction costs contain fixed costs, a cost proportional to the volume traded and a cost proportional to the value traded. Expected, the price of the European option decreases as the Hurst exponent increases. To achieve this goal, we estimate (Hurst parameter time series), on the real data to the desired result, the option price reduction reached. Comparing results show that the actual prices by fractional black-scholes model, is closer to the actual results.