8

Models for market risk factors

8.1 INTRODUCTION

In this chapter1 we present some models for market risk factors: all market variables, such as interest rates, credit spreads, FX rates, stock prices and commodity prices, are affecting the payoff of most of the contracts a bank has on its balance sheet. Effective and parsimonious models are required to allow simulation of the cash flows of contracts linked to the different market variables, which become risk factors in themselves.

We first introduce models that can be used to model the evolution of FX rates and equities, then we dwell on interest rate models and default models, which are the basis for the modelling of credit spreads. We do not focus on all market variables (e.g., we do not analyse inflation modelling), but hopefully we will cover the vast majority of the market risk factors that affect the cash flows of contracts.

The second part of the chapter, from Section 8.5 on, is devoted to application of the models to liquidity risk management.

8.2 STOCK PRICES AND FX RATES

A standard way to model the evolution of stock prices and FX rates is to assume that they are commanded by a geometric Brownian motion. A process xt follows a geometric Brownian motion if it described by the dynamics

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where μ and σ are, respectively, the constant drift and the volatility of the process, and Wt is a Brownian process. The differential ...

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