Uncovering Hidden Insights with Long-Memory Process Detection: An In-Depth Overview

Hassani, Hossein; Yarmohammadi, Masoud; Mashhad, Leila Marvian

doi:10.3390/risks11060113

Cited by 4 publications

(2 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…All of the above studies are conducted under the models driven by standard Brownian motion which are Markovian or memoryless. However, many studies show that asset price fluctuations exhibit "long memory" [12][13][14][15][16][17][18] or "short memory" [19][20][21][22] which can be captured by stochastic volatility models driven by fractional Brownian motion with the Hurst index H ∈ (1/2, 1) or H ∈ (0, 1/2), respectively. In addition, jumps in the asset price were observed by Coqueret and Tavin [23], Jin and Hong [24], Bates [25], and Wang and Xia [26].…”

Section: Introductionmentioning

confidence: 99%

Forward Starting Option Pricing under Double Fractional Stochastic Volatilities and Jumps

Zhang,

Xiao,

Yong

2024

Fractal Fract

View full text Add to dashboard Cite

This paper aims to provide an effective method for pricing forward starting options under the double fractional stochastic volatilities mixed-exponential jump-diffusion model. The value of a forward starting option is expressed in terms of the expectation of the forward characteristic function of log return. To obtain the forward characteristic function, we approximate the pricing model with a semimartingale by introducing two small perturbed parameters. Then, we rewrite the forward characteristic function as a conditional expectation of the proportion characteristic function which is expressed in terms of the solution to a classic PDE. With the affine structure of the approximate model, we obtain the solution to the PDE. Based on the derived forward characteristic function and the Fourier transform technique, we develop a pricing algorithm for forward starting options. For comparison, we also develop a simulation scheme for evaluating forward starting options. The numerical results demonstrate that the proposed pricing algorithm is effective. Exhaustive comparative experiments on eight models show that the effects of fractional Brownian motion, mixed-exponential jump, and the second volatility component on forward starting option prices are significant, and especially, the second fractional volatility is necessary to price accurately forward starting options under the framework of fractional Brownian motion.

show abstract

Section: Introductionmentioning

confidence: 99%

Forward Starting Option Pricing under Double Fractional Stochastic Volatilities and Jumps

Zhang,

Xiao,

Yong

2024

Fractal Fract

View full text Add to dashboard Cite

show abstract

“…Many studies [1][2][3][4][5] suggest that asset price fluctuations exhibit "long memory". In addition, recent empirical studies [6][7][8][9] show that the roughness of the volatility process is observed.…”

Section: Introductionmentioning

confidence: 99%

Option Pricing with Fractional Stochastic Volatilities and Jumps

Zhang,

Yong,

Xiao

2023

Fractal Fract

View full text Add to dashboard Cite

Empirical studies suggest that asset price fluctuations exhibit “long memory”, “volatility smile”, “volatility clustering” and asset prices present “jump”. To fit the above empirical characteristics of the market, this paper proposes a fractional stochastic volatility jump-diffusion model by combining two fractional stochastic volatilities with mixed-exponential jumps. The characteristic function of the log-return is expressed in terms of the solution of two-dimensional fractional Riccati equations of which closed-form solution does not exist. To obtain the explicit characteristic function, we approximate the pricing model by a semimartingale and convert fractional Riccati equations into a classic PDE. By the multi-dimensional Feynman-Kac theorem and the affine structure of the approximate model, we obtain the solution of the PDE with which the explicit characteristic function and its cumulants are derived. Based on the derived characteristic function and Fourier cosine series expansion, we obtain approximate European options prices. By differential evolution algorithm, we calibrate our approximate model and its two nested models to S&P 500 index options and obtain optimal parameter estimates of these models. Numerical results demonstrate the pricing method is fast and accurate. Empirical results demonstrate our approximate model fits the market best among the three models.

show abstract

Exploring the Depths of the Autocorrelation Function: Its Departure from Normality

Hassani,

Royer-Carenzi,

Mashhad

et al. 2024

Information

View full text Add to dashboard Cite

In this article, we study the autocorrelation function (ACF), which is a crucial element in time series analysis. We compare the distribution of the ACF, both from a theoretical and empirical point of view. We focus on white noise processes (WN), i.e., uncorrelated, centered, and identically distributed variables, whose ACFs are supposed to be asymptotically independent and converge towards the same normal distribution. But, the study of the sum of the sample ACF contradicts this property. Thus, our findings reveal a deviation of the sample ACF from normality beyond a specific lag. Note that this phenomenon is observed for white noise of varying lengths, and evenforn the residuals of an ARMA(p,q) model. This discovery challenges traditional assumptions of normality in time series modeling. Indeed, when modeling a time series, the crucial step is to validate the estimated model by checking that the associated residuals form white noise. In this study, we show that the widely used portmanteau tests are not completely accurate. Box–Pierce appears to be too conservative, whereas Ljung–Box is too liberal. We suggest an alternative method based on the ACF for establishing the reliability of the portmanteau test and the validity of the estimated model. We illustrate our methodology using money stock data in the USA.

show abstract

Uncovering Hidden Insights with Long-Memory Process Detection: An In-Depth Overview

Cited by 4 publications

References 17 publications

Forward Starting Option Pricing under Double Fractional Stochastic Volatilities and Jumps

Forward Starting Option Pricing under Double Fractional Stochastic Volatilities and Jumps

Option Pricing with Fractional Stochastic Volatilities and Jumps

Exploring the Depths of the Autocorrelation Function: Its Departure from Normality

Contact Info

Product

Resources

About