Optimally pricing European options with real distributions

Abstract

Most option pricing methods use mathematical distributions to approximate underlying asset, behavior. However, it is difficult to approximate the real distribution using pure mathematical distribution approaches. This study first introduces an innovative computational method of pricing European options based on the real distributions of the underlying asset. This computational approach can also be applied to expected value related applications that require real distributions rather than mathematical distributions. The contributions of this study include the following: a) it solves the risk neutral issue related to price options with real distributions, b) it proposes a simple method adjusting the standard deviation according to the practical need to apply short term volatility to real world applications and c) it demonstrates that modern databases are capable of handling large amounts of sample data to provide efficient execution speeds.