Option pricing with time-changed Lévy processes

Physica A: Statistical Mechanics and its Applications

2017

Considering that financial assets returns exhibit leptokurtosis, asymmetry properties as well as clustering and heteroskedasticity effect, this paper substitutes the logarithm normal jumps in Heston stochastic volatility model by the classical tempered stable (CTS) distribution and normal tempered stable (NTS) distribution to construct stochastic volatility tempered stable Lévy processes (TSSV) model. The TSSV model framework permits infinite activity jump behaviors of return dynamics and time varying volatility consistently observed in financial markets through subordinating tempered stable process to stochastic volatility process, capturing leptokurtosis, fat tailedness and asymmetry features of returns. By employing the analytical characteristic function and fast Fourier transform (FFT) technique, the formula for probability density function (PDF) of TSSV returns is derived, making the analytical formula for foreign equity option (FEO) pricing available. High frequency financial returns data are employed to verify the effectiveness of proposed models in reflecting the stylized facts of financial markets. Numerical analysis is performed to investigate the relationship between the corresponding parameters and the implied volatility of foreign equity option.

“…Let α∈(0,1)∪ (1,2) to guarantee the finite quadratic variation, C, λ + and λ ->0, m∈R. The characteristic function of CTS distribution is calculated as follows:…”

Section: Infinite Activity Tempered Stable Lévy Processesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Pricing foreign equity option under stochastic volatility tempered stable Lévy processes

Physica A: Statistical Mechanics and its Applications

2017

“…Abundant evidence has contradicted the normal distribution assumption in returns distribution which exhibits leptokurtosis, asymmetry and volatility clustering phenomena, leading to stochastic jumps in stock prices. It has been demonstrated by Ait-Sahalia et al (2012) and Klingler et al (2013) that stochastic volatility and jumps are inherent components of stock price dynamics which play important roles in accounting for stylized facts in financial markets. Therefore, when constructing models to describe asset dynamics, it is necessary to incorporate both stochastic volatility and leptokurtosis components.…”

Section: Introductionmentioning

confidence: 99%

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

The North American Journal of Economics and Finance

2017

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.

“…Moreover, there is abundant evidence that volatility exhibits clustering and heteroskedasticity effect, leading to stochastic jumps in stock prices. It has been demonstrated by Ait-Sahalia and Jacod [3], Klingler [4] that stochastic volatility and jumps are inherent components of the stock price dynamics that play important roles in the explanation of the implied volatility smile in options. Many alternative models are developed to reflect the intrinsic characteristics of asset returns and volatility smile effects of option prices, as shown by Kou [5], Mozumder [6], Shi [7], and Abdelrazeq [8].…”

Section: Introductionmentioning

confidence: 99%

Option pricing for stochastic volatility model with infinite activity Lévy jumps

Physica A: Statistical Mechanics and its Applications

2016

The purpose of this paper is to apply the stochastic volatility model driven by infinite activity Lévy processes to option pricing which displays infinite activity jumps behaviors and time varying volatility that is consistent with the phenomenon observed in underlying asset dynamics. We specially pay attention to three typical Lévy processes that replace the compound Poisson jumps in Bates model, aiming to capture the leptokurtic feature in asset returns and volatility clustering effect in returns variance. By utilizing the analytical characteristic function and fast Fourier transform technique, the closed form formula of option pricing can be derived. The intelligent global optimization search algorithm called Differential Evolution is introduced into the above highly dimensional models for parameters calibration so as to improve the calibration quality of fitted option models. Finally, we perform empirical researches using both time series data and options data on financial markets to illustrate the effectiveness and superiority of the proposed method.