Results 51 to 60 of about 4,806 (143)

On small time asymptotics for rough differential equations driven by fractional Brownian motions

, 2014
We survey existing results concerning the study in small times of the density of the solution of a rough differential equation driven by fractional Brownian motions.
D Nualart, F Baudoin, F Baudoin, F Comte, F Comte, J Feng, J Gatheral, J Hull, L Coutin, LCG Rogers, M Gubinelli, M Hairer, P Friz, P Friz, P Friz, T Cass, T Cass, T Cass, T Lyons, T Lyons, Y Hu, Y Inahama   +21 more
core   +1 more source

Fractional diffusion models of option prices in markets with jumps. [PDF]

Most of the recent literature dealing with the modeling of financial assets assumes that the underlying dynamics of equity prices follow a jump process or a Lévy process. This is done to incorporate rare or extreme events not captured by Gaussian models.
Cartea, Álvaro, Castillo Negrete, Diego del   +1 more
core   +3 more sources

Analysing time-fractional exotic options via efficient local meshless method

Results in Physics, 2020
In this article, we analyse the numerical simulation of the time-fractional Black-Scholes model governing butterfly spread option, digital option and double barrier option.
Mustafa Inc, Muhammad Nawaz Khan, Imtiaz Ahmad, Shao-Wen Yao, Hijaz Ahmad, Phatiphat Thounthong   +5 more
doaj   +1 more source

A class of intrinsic parallel difference methods for time-space fractional Black–Scholes equation

Advances in Difference Equations, 2018
To quickly solve the fractional Black–Scholes (B–S) equation in the option pricing problems, in this paper, we construct pure alternative segment explicit–implicit (PASE-I) and pure alternative segment implicit–explicit (PASI-E) difference schemes for ...
Yue Li, Xiaozhong Yang, Shuzhen Sun
doaj   +1 more source

Implicit cubic B-spline scheme for the fractional Black-Scholes model with Caputo-Hadamard derivative [PDF]

Journal of Mahani Mathematical Research
In this study, we introduce a novel numerical scheme for solving the Black–Scholes equation endowed with a Caputo-Hadamard fractional time derivative. The temporal derivative is discretized via a finite-difference approach, ensuring both stability and ...
Roya Montazeri
doaj   +1 more source

Option Pricing in a Fractional Brownian Motion Environment [PDF]

The purpose of this paper is to obtain a fractional Black-Scholes formula for the price of an option for every t in [0,T], a fractional Black-Scholes equation and a risk-neutral valuation theorem if the underlying is driven by a fractional Brownian ...
Cipian Necula
core  

A Novel Fourth-Order Finite Difference Scheme for European Option Pricing in the Time-Fractional Black–Scholes Model

Mathematics
This paper addresses the valuation of European options, which involves the complex and unpredictable dynamics of fractal market fluctuations. These are modeled using the α-order time-fractional Black–Scholes equation, where the Caputo fractional ...
Xin Cai, Yihong Wang
doaj   +1 more source

A Framework for Derivative Pricing in the Fractional Black-Scholes Market [PDF]

The aim of this paper is to develop a framework for evaluating derivatives if the underlying of the derivative contract is supposed to be driven by a fractional Brownian motion with Hurst parameter greater than 0.5.
Ciprian Necula
core  

Review of the Fractional Black-Scholes Equations and Their Solution Techniques

Fractal and Fractional
The pioneering work in finance by Black, Scholes and Merton during the 1970s led to the emergence of the Black-Scholes (B-S) equation, which offers a concise and transparent formula for determining the theoretical price of an option. The establishment of
Hongmei Zhang, Mengchen Zhang, Fawang Liu, Ming Shen   +3 more
doaj   +1 more source

An Efficient Numerical Scheme for a Time-Fractional Black–Scholes Partial Differential Equation Derived from the Fractal Market Hypothesis

Fractal and Fractional
Since the early 1970s, the study of Black–Scholes (BS) partial differential equations (PDEs) under the Efficient Market Hypothesis (EMH) has been a subject of active research in financial engineering.
Samuel M. Nuugulu, Frednard Gideon, Kailash C. Patidar   +2 more
doaj   +1 more source