Models at Work: A Practitioner's Guide to Risk Management (Global Financial Markets) by Farid Jawwad

Author:Farid, Jawwad [Farid, Jawwad]
Language: eng
Format: epub
ISBN: 9781137371652
Publisher: Palgrave Macmillan
Published: 2013-12-13T00:00:00+00:00

While we can club equity, commodity and currency simulators in one category, interest rate simulators are a completely different animal.

First, because there is more than one way of modeling interest rates.

Equilibrium models and arbitrage free models

•An equilibrium model is based on a simplified macro model of interest rate drivers. For instance the CIR model assumes a mean reverting process (if rates go up, they must come down, if they come down they must go up) that makes assumptions about a long term average rate and an adjustment process that pulls interest rates back to the long term mean.

•An arbitrage free model is a model that calibrates the output of the model on day one to the existing interest rate environment so that there are no opportunities for mis-pricing or arbitrage on day one between the real world and the interest rate model. For example, the Black Derman and Toy (BDT) model calibrates the existing interest rate environment as represented by zero curves and the volatility at each point in the term structure with the model to project the entire forward rate term structure.

Second, because unlike a price tree there are a number of additional questions that need to be answered for an interest rate tree.

•Are you going to simulate one rate or the entire term structure? A single short rate projection model is built very differently than a multi-factor forward rate projection model.

•What are the drivers that will drive interest rate movement in your model? Economic, statistical or data set/model specific?

•How are you going to model these drivers? Assumptions, data sets, fit?

•Will your model be a theoretically correct model driven by fundamentals of economic theory?

•Or will it be a model that matches model prices at inception with market prices?

•If you do match market price, what is the process used to resolve differences between model prices and market prices? How do you calibrate your model to match market prices?

•How will you translate simulated interest rates into bond prices within your model? In addition to a rate lattice (tree) or simulator you will also need a linked bond pricing lattice or simulator.

Compared to a price generating tree or Monte Carlo simulator for equities, currencies and commodities, the same engine for an interest rate simulator also faces another interesting challenge. A conventional binomial tree assumes a constant risk free interest rate to hold throughout the length of the tree. The same assumption holds for a Monte Carlo simulator. When forecasting interest rates, how can you simulate and then use the same rate in the same model at the same time. The short answer is you can’t.

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