Equilibrium asset pricing under the Lévy process with stochastic volatility and moment risk premiums

Ruan, Xinfeng; Zhu, Wei; Huang, Jiexiang; Zhang, Jin E.

doi:10.1016/j.econmod.2015.12.030

Cited by 14 publications

(10 citation statements)

References 32 publications

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“…Moment risk premiums in finance involve the skewness swaps (p = 3) and kurtosis swaps (p = 4); pseudo-Zernike moments in image processing techniques could require, say, moment order up to 50 (see e.g. [25,26,27,28]). On the other hand, some problems only require a lower moment stability.…”

Section: 3)mentioning

confidence: 99%

On pth moment stabilization of hybrid systems by discrete-time feedback control

Dong

Mao

2017

Stochastic Analysis and Applications

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Since Mao initiated the study of stabilization of continuous-time hybrid stochastic differential equations (SDEs) by feedback controls based on discrete-time state observations in 2013, many authors have further studied and developed it. However, so far no work on the pth moment stabilization has been reported. This paper is to investigate how to stabilize a given unstable hybrid SDE by feedback controls based on discrete-time state observations, in the sense of H∞, asymptotic and exponential stability in pth moment for all p > 1. The main techniques used are constructions of the Lyapunov functionals and generalizations of inequalities

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Section: 3)mentioning

confidence: 99%

On pth moment stabilization of hybrid systems by discrete-time feedback control

Dong

Mao

2017

Stochastic Analysis and Applications

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“…The financial development and growth over last century has caused the role of volatility to change. Volatility derivatives generally are special financial tools which provide opportunities to display the financial market fluctuations and give methods to manage volatility risks for investors (see, e.g., [1,2,4,5,26,30,32,33,34]). They are traded for decision-making between long or short positions, trading spreads between realized and implied volatility, and hedging against volatility risks.…”

Section: Introductionmentioning

confidence: 99%

“…Of all volatility derivatives, variance swaps are written on underlying assets' historical volatility and they are related to previous standard deviation of financial returns involving a specified time period. Various theoretical results, numerical algorithms and applications have been studied extensively for variance swaps in the literature; for instance we refer the reader to [5,8,28,30,31,33] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Variance swaps under Lévy process with stochastic volatility and stochastic interest rate in incomplete markets

Yang,

Yue,

Huang

2017

Preprint

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This paper focuses on the pricing of the variance swap in an incomplete market where the stochastic interest rate and the price of the stock are respectively driven by Cox-Ingersoll-Ross model and Heston model with simultaneous Lévy jumps. By using the equilibrium framework, we obtain the pricing kernel and the equivalent martingale measure. Moreover, under the forward measure instead of the risk neural measure, we give the closed-form solution for the fair delivery price of the discretely sampled variance swap by employing the joint moment generating function of the underlying processes. Finally, we provide some numerical examples to depict that the values of variance swaps not only depend on the stochastic interest rates but also increase in the presence of jump risks.

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“…This type of distribution is equipped with more proper ability in capturing asymmetry, higher kurtosis and fatter tails than α stable distribution, whose tail distributions are too thick to capture empirical tail behaviors in markets. Moreover, its infinite activity characteristic can better describe the infinite jumps phenomenon exists in the underlying process (Gajda et al, 2013;Ruan, 2016). In addition, the attainability of closed form characteristic functions of Lévy processes makes it possible for deriving density functions of these distributions employing fast Fourier transform method as well as calculating value at risk and conditional value at risk.…”

Section: Introductionmentioning

confidence: 99%

Measuring financial risk and portfolio reversion with time changed tempered stable Lévy processes

Gong

Xin-tian

2017

The North American Journal of Economics and Finance

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Given that underlying assets in financial markets exhibit stylized facts such as leptokurtosis, asymmetry, clustering properties and heteroskedasticity effect, this paper applies the stochastic volatility models driven by tempered stable Lévy processes to construct time changed tempered stable Lévy processes (TSSV) for financial risk measurement and portfolio reversion. The TSSV model framework permits infinite activity jump behaviors of returns dynamics and time varying volatility consistently observed in financial markets by introducing time changing volatility into tempered stable processes which specially refer to normal tempered stable (NTS) distribution as well as classical tempered stable (CTS) distribution, capturing leptokurtosis, fat tailedness and asymmetry features of returns in addition to volatility clustering effect in stochastic volatility. Through employing the analytical characteristic function and fast Fourier transform (FFT) technique, the closed form formulas for probability density function (PDF) of returns, value at risk (VaR) and conditional value at risk (CVaR) can be derived. Finally, in order to forecast extreme events and volatile market, we perform empirical researches on Hangseng index to measure risks and construct portfolio based on risk adjusted reward risk stock selection criteria employing TSSV models, with the stochastic volatility normal tempered stable (NTSSV) model producing superior performances relative to others.

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Equilibrium asset pricing under the Lévy process with stochastic volatility and moment risk premiums

Cited by 14 publications

References 32 publications

On pth moment stabilization of hybrid systems by discrete-time feedback control

On pth moment stabilization of hybrid systems by discrete-time feedback control

Variance swaps under Lévy process with stochastic volatility and stochastic interest rate in incomplete markets

Measuring financial risk and portfolio reversion with time changed tempered stable Lévy processes

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