Valuation of American Equity Options with Quadratic Approximation Models Adopting Fractional Brownian Motion

In this article, we compare the accuracy of the American approximation models: MBAW model (Macmillian, 1986; Barone-Adesi and Whaley, 1987) and MQuad model (Ju and Zhong, 1999) as well as the Black-Scholes (BS) model adopting fractional Brownian Motion (fBm) for three financial companies' equity put options data for the period from January 2004 to February 2010. The degree of accuracy is measured according to moneyness, variance estimate, and maturity. We find that the models occupied with fBm are more accurate and stable than the corresponding models across the board. In particular, there is a great advantage of using the fBm-based models when historical volatility is used. Even though the fractional Black-Scholes (FBS) model is for pricing European options, it is the best choice for long term maturity options. The FBS model is also capable of correcting the overestimation of the B-S model.