Mirror-time diffusion discount model of options pricing

TL;DR

This paper introduces a novel mirror-time diffusion discount model for options pricing that improves upon traditional models by incorporating a new distribution and ensuring self-calibration with historical data.

Contribution

It presents a self-calibrating options pricing model using mirror-time diffusion, addressing efficiency, completeness, and tail behavior in the distribution.

Findings

Model aligns with historical volatility data

Distribution lacks long tails and is unbiased for S&P 100 data

Theoretically produces skews matching interest rate derivatives

Abstract

The proposed model modifies option pricing formulas for the basic case of log-normal probability distribution providing correspondence to formulated criteria of efficiency and completeness. The model is self-calibrating by historic volatility data; it maintains the constant expected value at maturity of the hedged instantaneously self-financing portfolio. The payoff variance dependent on random stock price at maturity obtained under an equivalent martingale measure is taken as a condition for introduced "mirror-time" derivative diffusion discount process. Introduced ksi-return distribution, correspondent to the found general solution of backward drift-diffusion equation and normalized by theoretical diffusion coefficient, does not contain so-called "long tails" and unbiased for considered 2004-2007 S&P 100 index data. The model theoretically yields skews correspondent to practical term structure for interest rate derivatives. The method allows increasing the number of asset price probability distribution parameters.