scholarly journals NO ARBITRAGE UNDER TRANSACTION COSTS, WITH FRACTIONAL BROWNIAN MOTION AND BEYOND

2006 ◽  
Vol 16 (3) ◽  
pp. 569-582 ◽  
Author(s):  
Paolo Guasoni
Keyword(s):  
Brownian Motion ◽  
Transaction Costs ◽  
Fractional Brownian Motion ◽  
No Arbitrage

scholarly journals Asian Option Pricing with Transaction Costs and Dividends under the Fractional Brownian Motion Model

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Yan Zhang ◽  
Di Pan ◽  
Sheng-Wu Zhou ◽  
Miao Han
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Brownian Motion ◽  
Transaction Costs ◽  
Fractional Brownian Motion ◽  
Asian Option ◽  
Partial Differential ◽  
No Arbitrage ◽  
Geometric Average ◽  
Brownian Motion Model

The pricing problem of geometric average Asian option under fractional Brownian motion is studied in this paper. The partial differential equation satisfied by the option’s value is presented on the basis of no-arbitrage principle and fractional formula. Then by solving the partial differential equation, the pricing formula and call-put parity of the geometric average Asian option with dividend payment and transaction costs are obtained. At last, the influences of Hurst index and maturity on option value are discussed by numerical examples.

scholarly journals Shadow prices, fractional Brownian motion, and portfolio optimisation under transaction costs

2017 ◽  
Vol 22 (1) ◽  
pp. 161-180 ◽  
Author(s):  
Christoph Czichowsky ◽  
Rémi Peyre ◽  
Walter Schachermayer ◽  
Junjian Yang
Keyword(s):  
Brownian Motion ◽  
Transaction Costs ◽  
Fractional Brownian Motion ◽  
Portfolio Optimisation ◽  
Shadow Prices

scholarly journals FRACTIONAL WHITE NOISE CALCULUS AND APPLICATIONS TO FINANCE

2003 ◽  
Vol 06 (01) ◽  
pp. 1-32 ◽  
Author(s):  
YAOZHONG HU ◽  
BERNT ØKSENDAL
Keyword(s):  
Brownian Motion ◽  
White Noise ◽  
Fractional Brownian Motion ◽  
Standard Brownian Motion ◽  
Stochastic Integration ◽  
European Option ◽  
No Arbitrage ◽  
Black Scholes ◽  
White Noise Calculus ◽  
Replicating Portfolio

The purpose of this paper is to develop a fractional white noise calculus and to apply this to markets modeled by (Wick–) Itô type of stochastic differential equations driven by fractional Brownian motion BH(t); 1/2 < H < 1. We show that if we use an Itô type of stochastic integration with respect to BH(t) (as developed in Ref. 8), then the corresponding Itô fractional Black–Scholes market has no arbitrage, contrary to the situation when the pathwise integration is used. Moreover, we prove that our Itô fractional Black–Scholes market is complete and we compute explicitly the price and replicating portfolio of a European option in this market. The results are compared to the classical results based on standard Brownian motion B(t).

scholarly journals Lookback Option Pricing with Fixed Proportional Transaction Costs under Fractional Brownian Motion

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Jiao-Jiao Sun ◽  
Shengwu Zhou ◽  
Yan Zhang ◽  
Miao Han ◽  
Fei Wang
Keyword(s):  
Brownian Motion ◽  
Transaction Costs ◽  
Fractional Brownian Motion ◽  
Asset Price ◽  
Brownian Motion Process ◽  
Proportional Transaction Costs ◽  
Cost Rate ◽  
Lookback Option ◽  
Fixed Proportion ◽  
The Impact

The pricing problem of lookback option with a fixed proportion of transaction costs is investigated when the underlying asset price follows a fractional Brownian motion process. Firstly, using Leland’s hedging method a partial differential equation satisfied by the value of the lookback option is derived. Then we obtain its numerical solution by constructing a Crank-Nicolson format. Finally, the effectiveness of the proposed form is verified through a numerical example. Meanwhile, the impact of transaction cost rate and volatility on lookback option value is discussed.

Pricing of perpetual American put option with sub-mixed fractional Brownian motion

2019 ◽  
Vol 22 (4) ◽  
pp. 1145-1154
Author(s):  
Feng Xu ◽  
Shengwu Zhou
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Asset Price ◽  
Put Options ◽  
No Arbitrage ◽  
American Put Option ◽  
Put Option ◽  
American Put Options ◽  
Mixed Fractional Brownian Motion ◽  
American Put

Abstract The pricing problem of perpetual American put options is investigated when the underlying asset price follows a sub-mixed fractional Brownian motion process. First of all, the sub-mixed fractional Black-Scholes partial differential equation is established by using the delta hedging method and the principle of no arbitrage. Then, by solving the free boundary problem, we get the pricing formula of the perpetual American put option.

scholarly journals PRICING DERIVATIVES IN HERMITE MARKETS

2019 ◽  
Vol 22 (06) ◽  
pp. 1950031
Author(s):  
STOYAN V. STOYANOV ◽  
SVETLOZAR T. RACHEV ◽  
STEFAN MITTNIK ◽  
FRANK J. FABOZZI
Keyword(s):  
Brownian Motion ◽  
Financial Markets ◽  
Fractional Brownian Motion ◽  
Trading Strategies ◽  
Risky Assets ◽  
No Arbitrage ◽  
Arbitrage Opportunities ◽  
Black Scholes ◽  
Hedging Portfolio ◽  
New Framework

We present a new framework for Hermite fractional financial markets, generalizing the fractional Brownian motion (FBM) and fractional Rosenblatt markets. Considering pure and mixed Hermite markets, we introduce a strategy-specific arbitrage tax on the rate of transaction volume acceleration of the hedging portfolio as the prices of risky assets change, allowing us to transform Hermite markets with arbitrage opportunities to markets with no arbitrage opportunities within the class of Markov trading strategies. We derive PDEs for the price of such strategies in the presence of an arbitrage tax in pure Hermite, mixed Hermite, and Black–Scholes–Merton diffusion markets.

Pricing European options and currency options by time changed mixed fractional Brownian motion with transaction costs

2016 ◽  
Vol 03 (01) ◽  
pp. 1650003 ◽  
Author(s):  
Foad Shokrollahi ◽  
Adem Kılıçman ◽  
Marcin Magdziarz
Keyword(s):  
Brownian Motion ◽  
Transaction Costs ◽  
Fractional Brownian Motion ◽  
Discrete Time ◽  
Empirical Studies ◽  
Time Step ◽  
Currency Option ◽  
Mixed Fractional Brownian Motion ◽  
Text Model ◽  
The Impact

This study investigates a new formula for option pricing with transaction costs in a discrete time setting. The value of the financial assets is based on time-changed mixed fractional Brownian motion [Formula: see text] model. The pricing method is obtained for European call option using the time-changed [Formula: see text] model in a discrete time setting. Particularly, the minimal value [Formula: see text] of an option respect to transaction costs is obtained. Furthermore, the new model for pricing currency option is presented by utilizing the time-changed [Formula: see text] model. In addition, the impact of time step [Formula: see text], Hurst parameter H and transaction costs [Formula: see text] are also investigated, which substantiate that these parameters play a significant role in our pricing formula. Finally, the empirical studies and the simulation findings corroborate the theoretical bases and indicate the time-changed [Formula: see text] is a satisfactory model.

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