The Effectiveness of a Predictor-corrector Technique in European Currency Option Valuation

In this work, we adopt a predictor-corrector technique to examine the accuracy of the Fractional Black-Scholes (FBS) model. Compared to the standard Black-Scholes (B-S) model, FBS model involves one additional parameter, a Hurst value (H) providing information whether the time series exhibits persistent or anti-persistent behavior. The FBS model, as a result, has been shown to provide more accurate predictions of option price [Heo et al. (2017) and reference therein]. Estimation accuracy of volatility and H values are key to better option price estimates. However, volatility and Hurst values are unknown prior to the closing time; consequently, the estimation of option prices relies heavily on the accuracy of volatilities and Hurst parameter estimation. In this study we compare option price estimation accuracy using three variations of calculating H values, and two volatility measures. We estimate two H values using historic data using one-month data (21 trading days) and three-month data (63 trading days), respectively, and by using predicted volatility estimates obtained using a binomial method, as a predictor and then used them to estimate implied H values. We subsequently correct the predicted volatility measure using the implied H value, the predictor-corrector technique. We investigate the accuracy of these FBS models and examine effectiveness of this predictor-corrector technique using Euro currency option (XDE) data traded in NASDAQ from November 2007 to June 2016.