# Computational method for probability distribution on recursive relationships in financial applications

## TL;DR

This paper introduces a recursive computational method to accurately determine probability distributions of functions of observed financial data, applicable to various financial instruments and statistical tests.

## Contribution

It presents a novel recursive approach for calculating distributions in financial applications, improving accuracy over existing methods.

## Key findings

- High accuracy demonstrated in numerical experiments
- Applicable to diverse financial functions and instruments
- Efficient recursive computation method

## Abstract

In quantitative finance, it is often necessary to analyze the distribution of the sum of specific functions of observed values at discrete points of an underlying process. Examples include the probability density function, the hedging error, the Asian option, and statistical hypothesis testing. We propose a method to calculate such a distribution, utilizing a recursive method, and examine it using various examples. The results of the numerical experiment show that our proposed method has high accuracy.