Option Pricing under Double Heston Jump-Diffusion Model with Approximative Fractional Stochastic Volatility

Chang, Yuan; Wang, Yiming

doi:10.3390/math9020126

Cited by 5 publications

(4 citation statements)

References 35 publications

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“…Additionally, Approximation Fractional Brownian motion [27] emerged as a viable alternative, and Thao [27] demonstrated that it constitutes a semimartingale. This has led to increased interest in fractional stochastic volatility models among experts and academics [11], with many researchers incorporating Approximation Fractional Brownian motion in constructing stochastic volatility models [6].…”

Section: Introductionmentioning

confidence: 99%

Valuing European Option Under Double 3/2-Volatility Jump-Diffusion Model With Stochastic Interest Rate and Stochastic Intensity Under Approximative Fractional Brownian Motion

Bayad,

El Hajaj,

Hilal

2023

Int. J. Anal. Appl.

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In this study, we propose a more comprehensive and realistic option pricing model based on approximative fractional Brownian motion, building upon recent advancements in this area. Specifically, we utilize the double 3/2-volatility Jump-Diffusion model, which incorporates approximative fractional Brownian motion with 3/2-volatility, stochastic interest rate, and stochastic intensity. To account for the stochastic interest rate, we employ a two-factor Vasicek model. Notably, our model accommodates negative interest rates. Consequently, we develop a multi-factor model with a stochastic interest rate structure for pricing European options and derive a closed-form pricing formula with an analytical solution by applying some algebraic calculations and Lie symmetries. In order to demonstrate the superiority of our proposed model over other classical approaches, we present numerical results that showcase the value of a European call option. This comparative analysis underscores the advantages of our model in comparison to traditional models.

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Section: Introductionmentioning

confidence: 99%

Valuing European Option Under Double 3/2-Volatility Jump-Diffusion Model With Stochastic Interest Rate and Stochastic Intensity Under Approximative Fractional Brownian Motion

Bayad,

El Hajaj,

Hilal

2023

Int. J. Anal. Appl.

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“…However, the formula has made many assumptions in advance, for example, the volatility and interest rate of options are assumed to be a constant; the underlying asset follow geometric Brownian motion, etc., is not completely consistent with the actual market situation; thus, the option price calculated by the formula is far from the actual situation. Later, many scholars made corresponding improvements to the model, such as adjusting the time course of the evolution of the underlying asset price, and the interest rate and volatility were subject to a random process [2][3][4][5][6][7][8][9][10][11][12][13][14][15] so as to establish option pricing models closer to the actual situation, such as the CIR model [16,17] and Heston model [18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Dual-Hybrid Modeling for Option Pricing of CSI 300ETF

2022

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The reasonable pricing of options can effectively help investors avoid risks and obtain benefits, which plays a very important role in the stability of the financial market. The traditional single option pricing model often fails to meet the ideal expectations due to its limited conditions. Combining an economic model with a deep learning model to establish a hybrid model provides a new method to improve the prediction accuracy of the pricing model. This includes the usage of real historical data of about 10,000 sets of CSI 300 ETF options from January to December 2020 for experimental analysis. Aiming at the prediction problem of CSI 300ETF option pricing, based on the importance of random forest features, the Convolutional Neural Network and Long Short-Term Memory model (CNN-LSTM) in deep learning is combined with a typical stochastic volatility Heston model and stochastic interests CIR model in parameter models. The dual hybrid pricing model of the call option and the put option of CSI 300ETF is established. The dual-hybrid model and the reference model are integrated with ridge regression to further improve the forecasting effect. The results show that the dual-hybrid pricing model proposed in this paper has high accuracy, and the prediction accuracy is tens to hundreds of times higher than the reference model; moreover, MSE can be as low as 0.0003. The article provides an alternative method for the pricing of financial derivatives.

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“…The authors of several more recent research studies have proposed a number of GFBM extensions and adjustments, including the fractional Brownian motion model with adaptive parameters [68], irrational fractional Brownian motion model [69], fractional Brownian motion with two-variable Hurst exponent [70], or approximate fractional Brownian motion [71].…”

Section: Introductionmentioning

confidence: 99%

Efficient or Fractal Market Hypothesis? A Stock Indexes Modelling Using Geometric Brownian Motion and Geometric Fractional Brownian Motion

et al. 2021

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In this article, we propose a test of the dynamics of stock market indexes typical of the US and EU capital markets in order to determine which of the two fundamental hypotheses, efficient market hypothesis (EMH) or fractal market hypothesis (FMH), best describes market behavior. The article’s major goal is to show how to appropriately model return distributions for financial market indexes, specifically which geometric Brownian motion (GBM) and geometric fractional Brownian motion (GFBM) dynamic equations best define the evolution of the S&P 500 and Stoxx Europe 600 stock indexes. Daily stock index data were acquired from the Thomson Reuters Eikon database during a ten-year period, from January 2011 to December 2020. The main contribution of this work is determining whether these markets are efficient (as defined by the EMH), in which case the appropriate stock indexes dynamic equation is the GBM, or fractal (as described by the FMH), in which case the appropriate stock indexes dynamic equation is the GFBM. In this paper, we consider two methods for calculating the Hurst exponent: the rescaled range method (RS) and the periodogram method (PE). To determine which of the dynamics (GBM, GFBM) is more appropriate, we employed the mean absolute percentage error (MAPE) method. The simulation results demonstrate that the GFBM is better suited for forecasting stock market indexes than the GBM when the analyzed markets display fractality. However, while these findings cannot be generalized, they are verisimilar.

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Option Pricing under Double Heston Jump-Diffusion Model with Approximative Fractional Stochastic Volatility

Cited by 5 publications

References 35 publications

Valuing European Option Under Double 3/2-Volatility Jump-Diffusion Model With Stochastic Interest Rate and Stochastic Intensity Under Approximative Fractional Brownian Motion

Valuing European Option Under Double 3/2-Volatility Jump-Diffusion Model With Stochastic Interest Rate and Stochastic Intensity Under Approximative Fractional Brownian Motion

Dual-Hybrid Modeling for Option Pricing of CSI 300ETF

Efficient or Fractal Market Hypothesis? A Stock Indexes Modelling Using Geometric Brownian Motion and Geometric Fractional Brownian Motion

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