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A new option pricing method: Based on the perspective of sub-mixed fractional Brownian motion
YU Mei, CHENG Zhiyong, DENG Jun, WANG Shouyang
Systems Engineering - Theory & Practice ›› 2021, Vol. 41 ›› Issue (11) : 2761-2776.
PDF(882 KB)
PDF(882 KB)
A new option pricing method: Based on the perspective of sub-mixed fractional Brownian motion
To capture the "leptokurtosis and fat-tail", the long memory, and other fractal features of financial asset prices, in this paper, we use the time-varying sub-mixed fractional Brownian motion with GARCH structure to describe the dynamic change of risk asset price, besides, the martingale pricing theory is used to obtain the closed form of option price, which extends the traditional BS and fractional Brownian motion model. The US S&P500 Index Option, Korea KOSPI200 Index Option, China SSE 50 ETF Option, China Hong Kong Hang Seng Index Option, China Taiwan Index Option, and India NIFTY Index Option are used to conduct the empirical studies. Our finding shows that the time-varying sub-mixed fractional Brownian motion with GARCH structure has higher pricing accuracy than to BS and sub-mixed fractional Brownian motion model, which has particularly prominent pricing performance in the emerging markets. This research results have important theoretical and practical implication in several aspects, including the reasonable pricing of option, risk management and investment decision-making, and it also contributes to the development of multi-level capital market.
time-varying Hurst index / GARCH model / option pricing / sub-mixed fractional Brownian motion {{custom_keyword}} /
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National Natural Science Foundation of China (72071046); Fundamental Research Funds for the Central Universities in UIBE (19YB10)
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