Footnote:
Nach Informationen von SSRN wurde die ursprüngliche Fassung des Dokuments January 22, 2014 erstellt
Description:
Two methods to derive Hurst exponent from option prices are proposed in this paper. They are based on fractional Brownian market setting. The first method is to use fractional Black-Scholes model inversely to derive implied Hurst exponent. The second one depends on no specific option pricing model. It is a model-free approach which is applicable as long as asset price evolves with on jumps. The difficulty in deriving implied information from fractional Brownian market is due to the fact that both Hurst exponent and volatility are unobservable. So they can be derived as a whole from single-period option prices, but can hardly be separated from each other. In this paper, a method that integrates option prices of different maturities is suggested to solve this problem. We also make a comparison between volatility in classical Brownian market and that in fractional Brownian market, which reveals that variance term structures are fitted differently in two settings. Based on this result, we suggest two potential applications of implied Hurst exponent in this paper