Using computational methodology to price European options with actual payoff distributions

Most option pricing methods use mathematical distributions to approximate underlying asset behavior. However, pure mathematical distribution approaches have difficulty approximating the real distribution. This study first introduces an innovative computational method for pricing European options based on the real payoff distribution of the underlying asset. This computational approach can also be applied to applications related to expected value that require real distributions rather than mathematical distributions. This study makes the following contributions: (a) solving the risk neutral issue related to price options with real payoff distributions; (b) proposing a simple method for adjusting standard deviation based on the need to apply short term volatility to real world applications; (c) demonstrating an option pricing algorithm that is easy to apply to cross field applications.