Abstract
This study investigates European option pricing under fractional Brownian motion (fBm) and applies it to realized volatility (RV). The RV measure is selected because it uniquely exhibits simultaneous stationarity and long-range dependency properties in financial time series, as shown in our empirical study. Meanwhile, the Black-Scholes differential equation is not well defined when the underlying assets follow fBm with the Hurst exponent H not equal to 1/2 because fBm is not a semimartingale. Thus, we compute the European option prices using a previously proposed fractional Black-Scholes formula. Our empirical study is conducted on Tokyo Stock Price Index data from January 06, 1997 to December 30, 2013 with a sample size of 4177.
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