Pricing Using a Homogeneously Saturated Equation

TL;DR

This paper introduces a homogeneously saturated equation for asset pricing, incorporating Student's t-distributed noise, and demonstrates its effectiveness in modeling and option pricing compared to traditional models.

Contribution

It presents a novel homogeneously saturated equation for asset prices that accounts for realistic return limits and uses Student's t-distribution for noise, improving option pricing accuracy.

Findings

The model limits asset return ranges, making it more realistic.

Best-fit parameters for Student's t-distributions improve option pricing.

The approach offers a new perspective on asset and option valuation.

Abstract

A homogeneously saturated equation for the time development of the price of a financial asset is presented and investigated for the pricing of European call options using noise that is distributed as a Student's t-distribution. In the limit that the saturation parameter of the equation equals zero, the standard model of geometric motion for the price of an asset is obtained. The homogeneously saturated equation for the price of an asset is similar to a simple equation for the output of a homogeneously broadened laser. The homogeneously saturated equation tends to limit the range of returns and thus seems to be realistic. Fits to linear returns obtained from the adjusted closing values for the S&P 500 index were used to obtain best-fit parameters for Student's t-distributions and for normal distributions, and these fits were used to price options, and to compare approaches to modelling prices. This work has value in understanding the pricing of assets and of European call options.