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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Shrnutí: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.
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ISSN:1551-3203
1941-0050
DOI:10.1109/TII.2015.2500885