# Estimating the Counterparty Risk Exposure by using the Brownian Motion Local Time

## TL;DR

This paper introduces a novel method leveraging Brownian motion local time properties to efficiently estimate counterparty risk exposure in OTC derivatives, reducing computational costs.

## Contribution

It proposes a new approach using Brownian motion local time to simplify and speed up counterparty risk calculations in financial derivatives.

## Key findings

- Reduces computational effort in risk estimation.
- Provides a new analytical framework for risk measurement.
- Enhances efficiency of Basel II/III compliance procedures.

## Abstract

In recent years, the counterparty credit risk measure, namely the default risk in \emph{Over The Counter} (OTC) derivatives contracts, has received great attention by banking regulators, specifically within the frameworks of \emph{Basel II} and \emph{Basel III.} More explicitly, to obtain the related risk figures, one has first obliged to compute intermediate output functionals related to the \emph{Mark-to-Market} (MtM) position at a given time $t \in [0, T],$ T being a positive, and finite, time horizon. The latter implies an enormous amount of computational effort is needed, with related highly time consuming procedures to be carried out, turning out into significant costs. To overcome latter issue, we propose a smart exploitation of the properties of the (local) time spent by the Brownian motion close to a given value.