scholarly journals Pricing Currency Option in a Mixed Fractional Brownian Motion with Jumps Environment

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Foad Shokrollahi ◽  
Adem Kılıçman
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Brownian Motion ◽  
Exchange Rate ◽  
Fractional Brownian Motion ◽  
Fractional Partial Differential Equation ◽  
Currency Option ◽  
Mixed Fractional Brownian Motion ◽  
Spot Exchange Rate ◽  
New Framework

A new framework for pricing the European currency option is developed in the case where the spot exchange rate fellows a mixed fractional Brownian motion with jumps. The jump mixed fractional partial differential equation is obtained. Some Greeks and properties volatility are discussed. Finally the numerical simulations illustrate that our model is flexible and easy to implement.

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.

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.

scholarly journals Existence and exponential stability in the pth moment for impulsive neutral stochastic integro-differential equations driven by mixed fractional Brownian motion

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xia Zhou ◽  
Dongpeng Zhou ◽  
Shouming Zhong
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Exponential Stability ◽  
Fractional Brownian Motion ◽  
Mild Solutions ◽  
Semigroup Theory ◽  
Sufficient Conditions ◽  
Fractional Power ◽  
Banach Fixed Point Theorem ◽  
Mixed Fractional Brownian Motion

Abstract This paper consider the existence, uniqueness and exponential stability in the pth moment of mild solution for impulsive neutral stochastic integro-differential equations driven simultaneously by fractional Brownian motion and by standard Brownian motion. Based on semigroup theory, the sufficient conditions to ensure the existence and uniqueness of mild solutions are obtained in terms of fractional power of operators and Banach fixed point theorem. Moreover, the pth moment exponential stability conditions of the equation are obtained by means of an impulsive integral inequality. Finally, an example is presented to illustrate the effectiveness of the obtained results.

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