An empirical comparison of the bachelier and the black-scholes call option pricing models. - Kok, Wen Ya. (2009)
The Black-Scholes formula is a recognized model for pricing and hedging derivative securities. It relies, however, on several highly questionable assumptions. This report examines whether the Bachelier’s option pricing model can be used to find the European call option prices corresponding to the market prices better than the Black-Scholes option pricing model when the historical volatility is used. Both the Black-Scholes and the Bachelier’s models are applied to the at-the-money and in-the-money options of the AMEX and the CBOE Indexes European call options in the year 2005. As a benchmark, the Black-Scholes model with historical volatility estimates is used. Comparisons reveal that the Bachelier’s option pricing model outperforms the benchmark and exhibits higher precision than the Black-Scholes formula in pricing options, be it shorter or longer term options. Both models exhibit greater accuracy for options with shorter time to maturity and greater degree of moneyness.