Time-dependent Hurst exponent in traffic time series

Yue, Jianhai; Shang, Pengjian; Dong, Kuiran

doi:10.1109/icitis.2010.5689677

Cited by 1 publication

(1 citation statement)

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“…They discovered that the local scaling exponent of financial series exhibited significantly greater time-variability compared to artificial ones. In applications involving traffic, Yue et al [27] and Dong et al [5] proposed a novel approach known as the multi-dependent Hurst exponent to examine the correlation properties of the nonstationary time series where H τ (t) reflects the level of variability of time series at every time t and duration τ . Hence, a generalized Gaussian process with time-varying path smoothness is interesting from a theoretical standpoint and in a variety of applications.…”

Section: Introductionmentioning

confidence: 99%

European option pricing under a generalized fractional Brownian motion Heston exponential Hull-White model with transaction costs by the Deep Galerkin Method

Motameni,

Mehrdoust,

Najafi

2024

Preprint

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We propose a new financial model called the generalized fractional Brownian motion Heston exponential Hull-White model, which has stochastic volatility and interest rate, long memory, and heavy tail distribution. Based on the market price of the volatility and delta hedging strategies, we propose a partial differential equation (PDE) to obtain the European option price. To do this, portfolio changes contain long one position of the European call option and shares of the underlying assets (stock, zero coupon bond, volatility), where we use the mentioned model to obtain the price. Due to transaction costs, the resulting equation is a fully nonlinear PDE, which we use the Deep Galerkin Method (DGM) to solve it. Also, we present the proof of the convergence of the method to this class of equations, which includes two parts: the convergence of the loss function to zero and the convergence of the neural network to the exact solution of the equation. We finally present numerical results to show the model and method’s effectiveness.

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Section: Introductionmentioning

confidence: 99%