European Option Pricing With a Fast Fourier Transform Algorithm for Big Data Analysis

Several empirical studies show that, under multiple risks, markets exhibit many new properties, such as volatility smile and cluster fueled by the explosion of transaction data. This paper attempts to capture these newly developed features using the valuation of European options as a vehicle. Statis...

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Vydáno v:	IEEE transactions on industrial informatics Ročník 12; číslo 3; s. 1219 - 1231
Hlavní autoři:	Shuang Xiao, Shi-Hua Ma, Guo Li, Mukhopadhyay, Samar K.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Piscataway IEEE 01.06.2016 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Algorithm design and analysis Algorithms Analytical models Big data big data analysis Europe European option pricing Fast Fourier Transform algorithm Fourier transforms Markets Mathematical analysis Mathematical models Multiple risks Numerical analysis Numerical models Pricing Reversion stochastic modeling Stochastic processes Volatility stochastic modeling European option pricing Big data analysis fast Fourier transform (FFT) algorithm multiple risks
ISSN:	1551-3203, 1941-0050
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Abstract	Several empirical studies show that, under multiple risks, markets exhibit many new properties, such as volatility smile and cluster fueled by the explosion of transaction data. This paper attempts to capture these newly developed features using the valuation of European options as a vehicle. Statistical analysis performed on the data collected from the currency option market clearly shows the coexistence of mean reversion, jumps, volatility smile, and leptokurtosis and fat tail. We characterize the dynamics of the underlying asset in this kind of environment by establishing a coupled stochastic differential equation model with triple characteristics of mean reversion, nonaffine stochastic volatility, and mixed-exponential jumps. Moreover, we propose a characteristic function method to derive the closed-form pricing formula. We also present a fast Fourier transform (FFT) algorithm-based numerical solution method. Finally, extensive numerical experiments are conducted to validate both the modeling methodology and the numerical algorithm. Results demonstrate that the model behaves well in capturing the properties observed in the market, and the FFT numerical algorithm is both accurate and efficient in addressing large amount of data.
AbstractList	Several empirical studies show that, under multiple risks, markets exhibit many new properties, such as volatility smile and cluster fueled by the explosion of transaction data. This paper attempts to capture these newly developed features using the valuation of European options as a vehicle. Statistical analysis performed on the data collected from the currency option market clearly shows the coexistence of mean reversion, jumps, volatility smile, and leptokurtosis and fat tail. We characterize the dynamics of the underlying asset in this kind of environment by establishing a coupled stochastic differential equation model with triple characteristics of mean reversion, nonaffine stochastic volatility, and mixed-exponential jumps. Moreover, we propose a characteristic function method to derive the closed-form pricing formula. We also present a fast Fourier transform (FFT) algorithm-based numerical solution method. Finally, extensive numerical experiments are conducted to validate both the modeling methodology and the numerical algorithm. Results demonstrate that the model behaves well in capturing the properties observed in the market, and the FFT numerical algorithm is both accurate and efficient in addressing large amount of data.
Author	Mukhopadhyay, Samar K. Shi-Hua Ma Shuang Xiao Guo Li
Author_xml	– sequence: 1 surname: Shuang Xiao fullname: Shuang Xiao organization: Sch. of Manage., Huazhong Univ. of Sci. & Technol., Wuhan, China – sequence: 2 surname: Shi-Hua Ma fullname: Shi-Hua Ma organization: Sch. of Manage., Huazhong Univ. of Sci. & Technol., Wuhan, China – sequence: 3 surname: Guo Li fullname: Guo Li email: lg4229682@163.com organization: Sch. of Manage. & Econ., Beijing Inst. of Technol., Beijing, China – sequence: 4 givenname: Samar K. surname: Mukhopadhyay fullname: Mukhopadhyay, Samar K. organization: Grad. Sch. of Bus., Sungkyunkwan Univ., Seoul, South Korea
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SubjectTerms	Algorithm design and analysis Algorithms Analytical models Big data big data analysis Europe European option pricing Fast Fourier Transform algorithm Fourier transforms Markets Mathematical analysis Mathematical models Multiple risks Numerical analysis Numerical models Pricing Reversion stochastic modeling Stochastic processes Volatility
Title	European Option Pricing With a Fast Fourier Transform Algorithm for Big Data Analysis
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