scholarly journals Barrier Options and a Reflection Principle of the Fractional Brownian Motion

2003 ◽  
Author(s):  
Ciprian Necula
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Reflection Principle ◽  
Barrier Options

scholarly journals Randomized quasi Monte Carlo methods for pricing of barrier options under fractional Brownian motion

2019 ◽  
Vol 1255 ◽  
pp. 012019
Author(s):  
Chatarina Enny Murwaningtyas ◽  
Sri Haryatmi Kartiko ◽  
Gunardi ◽  
Herry Pribawanto Suryawan
Keyword(s):  
Monte Carlo ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Monte Carlo Methods ◽  
Barrier Options ◽  
Quasi Monte Carlo

A very efficient approach for pricing barrier options on an underlying described by the mixed fractional Brownian motion

2016 ◽  
Vol 87 ◽  
pp. 240-248 ◽  
Author(s):  
Luca Vincenzo Ballestra ◽  
Graziella Pacelli ◽  
Davide Radi
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Barrier Options ◽  
Efficient Approach ◽  
Mixed Fractional Brownian Motion

scholarly journals OPTIONS WITH UNDERLYING ASSET DRIVEN BY A FRACTIONAL BROWNIAN MOTION: CROSSING BARRIERS ESTIMATES

2010 ◽  
Vol 06 (01) ◽  
pp. 109-118 ◽  
Author(s):  
GIULIA ROTUNDO ◽  
ROY CERQUETI
Keyword(s):  
Brownian Motion ◽  
Decision Support ◽  
Fractional Brownian Motion ◽  
Barrier Options ◽  
Probability Estimate ◽  
Nonlinear Transformations ◽  
Underlying Asset ◽  
Speculative Bubbles ◽  
Future Work

This paper aims at supplying a decision support system tool to investors having options written on an underlying asset driven by a fractional Brownian motion (fBm). The results presented here rely on the theory of nonlinear transformations of fBm and provide the calculus of the probability estimate that the underlying asset crosses nonlinear barriers. Recent results stating a Black and Scholes-like pricing formula for fBm monitor the expected behaviour of options on the basis of the dynamics of the underlying asset. We rely on the results drawn for plain vanilla options, leaving their extension to barrier options for future work. The theory of speculative bubbles due to endogenous causes provides a useful suggestion for the detection of periods in which these results should be used. The application of the above results is shown through the NASDAQ case study.

scholarly journals A Wavelet-Based Almost-Sure Uniform Approximation of Fractional Brownian Motion with a Parallel Algorithm

2014 ◽  
Vol 51 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Dawei Hong ◽  
Shushuang Man ◽  
Jean-Camille Birget ◽  
Desmond S. Lun
Keyword(s):  
Brownian Motion ◽  
Convergence Rate ◽  
Fractional Brownian Motion ◽  
Parallel Algorithm ◽  
Uniform Approximation ◽  
Haar Wavelets ◽  
Hurst Index ◽  
Sample Paths ◽  
Vanishing Moment ◽  
Uniform Expansion

We construct a wavelet-based almost-sure uniform approximation of fractional Brownian motion (FBM) (Bt(H))_t∈[0,1] of Hurst index H ∈ (0, 1). Our results show that, by Haar wavelets which merely have one vanishing moment, an almost-sure uniform expansion of FBM for H ∈ (0, 1) can be established. The convergence rate of our approximation is derived. We also describe a parallel algorithm that generates sample paths of an FBM efficiently.

Pricing geometric asian power options in the sub-fractional brownian motion environment

2021 ◽  
Vol 145 ◽  
pp. 110754
Author(s):  
WEI WANG ◽  
GUANGHUI CAI ◽  
XIANGXING TAO
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion

Global attracting sets of neutral stochastic functional integro-differential equations driven by a fractional Brownian motion

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
A. Bakka ◽  
S. Hajji ◽  
D. Kiouach
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Brownian Motion ◽  
Differential Equations ◽  
Fractional Brownian Motion ◽  
Sufficient Conditions ◽  
Integrodifferential Equations ◽  
Hurst Parameter ◽  
Fixed Point Principle ◽  
Stochastic Functional

Abstract By means of the Banach fixed point principle, we establish some sufficient conditions ensuring the existence of the global attracting sets of neutral stochastic functional integrodifferential equations with finite delay driven by a fractional Brownian motion (fBm) with Hurst parameter H ∈ ( 1 2 , 1 ) {H\in(\frac{1}{2},1)} in a Hilbert space.

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