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Samar.jpg Area Decision Science
Faculty Samar Mukhopadhyay
Position Professor
Title European Option Pricing with a Fast Fourier Transform Algorithm for Big Data Analysis
Link
IEEE_Transaction_Paper.pdf
							Several empirical studies show that, under multiple risks like stochastic volatility and jump risks, markets
exhibit many new properties, such as volatility smile and cluster fueled by the explosion of transaction
data. The traditional Black-Scholes model fails to fit these newly-developed characteristics. This paper
attempts to capture these newer 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 existence 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, non-affine stochastic volatility and mixed-exponential
jumps. However, the traditional no-arbitrage option pricing theory no longer applies for analytical
solution of this model. Moreover, the commonly used Monte Carlo simulation to numerically calculate the
option prices takes a long time, especially for a huge amount of data. 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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