Probability distribution of returns in the Heston model with stochastic volatility*

Drăgulescu, Adrian; Yakovenko, Victor M.

doi:10.1080/14697688.2002.0000011

Cited by 166 publications

(180 citation statements)

References 45 publications

(95 reference statements)

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“…(5) is exact only when m 2 = k 2 /2α but Ref. [4] shows that this is not true for the Dow Jones. We will have thus to simulate the process to compute the leverage effect in each specific Heston case.…”

mentioning

confidence: 99%

A comparison between several correlated stochastic volatility models

Perelló

Masoliver

Anento

2004

Physica A: Statistical Mechanics and its Applications

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We compare the most common SV models such as the Ornstein-Uhlenbeck (OU), the Heston and the exponential OU (expOU) models. We try to decide which is the most appropriate one by studying their volatility autocorrelation and leverage effect, and thus outline the limitations of each model. We add empirical research on market indices confirming the universality of the leverage and volatility correlations.

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mentioning

confidence: 99%

A comparison between several correlated stochastic volatility models

Perelló

Masoliver

Anento

2004

Physica A: Statistical Mechanics and its Applications

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“…If b<0, the same result holds with b replaced by |b|. The exponential law has been found to describe well the distribution of financial returns at intermediate time scales, from hours to weeks, either in the tail (Mantegna and Stanley, 1995;Cont et al, 1997) and even over the full range (Laherrère and Sornette, 1998;Dragulescu. and Yakovenko, 2002 ;Silva and Yakovenko, 2003 ;Silva et al, 2004).…”

Section: Probability Density Function (Pdfmentioning

confidence: 48%

Properties of a simple bilinear stochastic model: Estimation and predictability

Sornette

Писаренко

2008

Physica D: Nonlinear Phenomena

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We analyze the properties of arguably the simplest bilinear stochastic multiplicative process, proposed as a model of financial returns and of other complex systems combining both nonlinearity and multiplicative noise. By construction, it has no linear predictability (zero two-point correlation) but a certain nonlinear predictability (non-zero three-point correlation). It can thus be considered as a paradigm for testing the existence of a possible nonlinear predictability in a given time series. We present a rather exhaustive study of the process, including its ability to produce fat-tailed distribution from Gaussian innovations, the unstable characteristics of the inversion of the key nonlinear parameters and of the two initial conditions necessary for the implementation of a prediction scheme and an analysis of the associated super-exponential sensitivity of the inversion of the innovations in the presence of a large impulse. Our study emphasizes the conditions under which a degree of predictability can be achieved and describe a number of different attempts, which overall illuminates the properties of the process. In conclusion, notwithstanding its remarkable simplicity, the bilinear stochastic process exhibits remarkably rich and complex behavior, which makes it a serious candidate for the modeling of financial time series among others. IntroductionDaily asset returns in liquid markets exhibit two key statistical properties: (i) price changes are not auto-correlated beyond a few minutes, but (ii) the absolute values of changes are autocorrelated over long time scales leading to long-term persistence of the volatility. Hsieh (1995) noted that nonlinear processes can generate this type of behavior while linear process cannot. Volatility clustering, also called ARCH effect (Engle, 1982) is a clear manifestation of the existence of non-linear dependences between returns observed at different lags. (FI)-GARCH (Baillie et al

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“…This work is the sequel to our former work (Palupi et al, 2014) and is in line with the work of (Dragulescu and Yakovenko, 2002). In this study, the stock price under consideration is assumed to follow geometric Brownian motion and the variance (the square of volatility) is assumed to follow Ornstein-Uhlenbeck process as in Heston model (Heston, 1993).…”

Section: Introductionmentioning

confidence: 74%

Comparing the Empirical and the Theoretical Probability Density of Return in which Variance Obeying Ornstein-Uhlenbeck Process at Indonesian Stock Exchange IDX

Palupi¹,

Tandelilin²,

Hermanto³

et al. 2017

American Journal of Applied Sciences

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The distribution of the probability density of a return index with stochastic volatility has been calculated. Here the stock index is assumed to follow geometric Brownian motion, while the variance is assumed to obey Ornstein-Uhlenbeck process as in Heston model. The distribution of the probability density of the return which is obtained by solving the FokkerPlanck equation of two dimensional index and the variance have been compared with the probability density taken from Indonesian Stock Exchange (IDX). In this study, we use Jakarta Islamic Index (JII), LQ45 and Jakarta Composite Index (JCI) data series from 2004 to 2012. We have shown that the theoretical probability density of return obtained from the calculation is in agreement with the empirical probability density. The theoretical probability density with stochastic volatility is closer to the empirical one than that of the Gaussian, particularly at the tail. The variance probability density at stationary state can be obtained by fitting the empirical probability density obtained from IDX data series with an integral expression obtained from quantum mechanical method.

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Probability distribution of returns in the Heston model with stochastic volatility*

Cited by 166 publications

References 45 publications

A comparison between several correlated stochastic volatility models

A comparison between several correlated stochastic volatility models

Properties of a simple bilinear stochastic model: Estimation and predictability

Comparing the Empirical and the Theoretical Probability Density of Return in which Variance Obeying Ornstein-Uhlenbeck Process at Indonesian Stock Exchange IDX

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