Pricing European Style Options
Posted: 31 Aug 2015 Last revised: 13 Sep 2018
Date Written: February 24, 2018
The Black-Scholes option model created a revolution in finance. It was perceived that the model opened up a methodology to price option contracts. The methodology has been problematic as numerous empirical contradictions and anomalies have been noted. Born out of Frequentist decision theory, a key assumption in the formula is that all parameters are known. When viewed as an estimator, however, it is shown that it does not converge to a population parameter. Consequently, a new model is built using Bayesian decision theory rather than Frequentist decision theory. This is done as it assures that the estimator will be both admissible and coherent, something that cannot generally happen with existing methods using Ito calculus or binomial trees. The model proposed is derived in two distinct ways. The first is both distribution-free and presumes no first moment. The second follows the work of Harris in deriving the density functions of various asset classes. The former should be robust, the later, powerful.
Keywords: option pricing, Black-Scholes, Cauchy distribution, mean-variance finance, European style options
JEL Classification: G00, G13
Suggested Citation: Suggested Citation