A New Distribution-Random Limit Normal Distribution

TL;DR

This paper proposes a novel distribution derived from the normal distribution using heat equations to better model tail risks, validated with market data.

Contribution

It introduces a new distribution based on heat equations to enhance tail risk modeling capabilities.

Findings

Model effectively captures tail risks in market data

New distribution outperforms classical normal in risk estimation

Validated with empirical market data

Abstract

This paper introduces a new distribution to improve tail risk modeling. Based on the classical normal distribution, we define a new distribution by a series of heat equations. Then, we use market data to verify our model.