Barrie & Hibbert Knowledge Base

Real-rate and inflation calibration: Changes for the end March 2010 calibration

2010-03-16T16:09:20Z

This note explains our approach to Market Consistent and Real World real interest rate calibrations. In our ESG models, inflation is derived by subtracting real from nominal interest rates. Any changes to the real rate calibration approach will have an impact on inflation. We highlight some changes to our calibration approach which will be introduced at end-March 2010.

Calibrating the Dividend Yield Model

2010-03-16T16:00:35Z

This note explains our methodology to calibrate the dividend yield model for a broad-based large mid cap equity index. In our ESG model this corresponds to the parent equity asset (E_Economy).

The calibration outlined applies to a stochastic model for dividend yields used in our ESG models. Dividend yield is modelled as a stochastic log normal mean-reverting autoregressive process. While simple the dividend yield model is tractable yet flexible enough to provide distributions consistent with historical data.

Real World Credit Calibration: Credit target update Q1 2010

2010-03-15T12:48:40Z

This document details our latest update to the Barrie and Hibbert real-world credit rating transition matrix in order to reflect 2009 credit events. This transition matrix will be used in our ESG calibrations from the end of March 2010 onwards. To assess the relative effect of this update on simulated ESG default rates, we also analyse the distributional properties of default rates under the old and new matrix.

We also provide our end December 2009 targets for the unconditional distribution of corporate credit spreads of different ratings.

Real-world equity calibration: a comparison of realised and expected volatility

2010-03-15T12:29:16Z

This note compares realised volatility with different measures of expected equity volatility. Realised equity volatility is the sum of expected and unexpected equity volatility. It is unobservable and we need to rely on an estimator. Any estimate will contain sampling and measurement error. It is also hard to decompose realised volatility into expected and unexpected volatility as volatility expectations are unobservable.

End March 2010 - Pre-Calibration Note

2010-03-12T11:11:51Z

This note sets out the planned delivery schedule for our end March 2010 standard calibrations, and also gives details of any changes to calibration methodology and coverage.

Real-world credit calibration: Modelling credit risky sovereign bonds

2010-03-11T14:35:28Z

In this note, we will summarise different options that can be used to model sovereign credit risky debt in our ESG models. This is particularly pertinent to the Eurozone where there is a common currency, whilst debt issued by different member states is currently trading at a wide range of spreads.

Pass-through mortgage-backed securities: Model description and calibration

2010-03-04T13:42:22Z

This note describes the pass-through mortgage-backed securities model and its calibration to US market data. Version 2.0

Mortgage backed securities calibration, USD end December 2009

2010-03-02T12:22:05Z

This note describes the mortgage-backed securities (MBS) calibration methodology and presents the calibration parameters for USD as at the end of December 2009.

Low discrepancy numbers and their use within the ESG

2010-02-15T15:04:36Z

The Barrie & Hibbert ESG (Economic Scenario Generator) uses a Monte Carlo scheme to determine distributions and expectations of various financial and/or economic quantities by running a large number of trials (scenarios). Within the ESG this involves the generation of pseudo-random numbers, which are mapped into shocks and used to represent the stochastic (uncertain) aspects of the simulation. This study considers the effect of replacing the pseudo-random numbers with an alternative source of numbers (low-discrepancy numbers) that are not random, in an effort to improve the efficiency of the ESG.

Under certain conditions the use of low-discrepancy numbers is shown to result in faster convergence of the simulation. This means that fewer trials are necessary to obtain the same level of accuracy, or greater accuracy can be achieved with the same number of trials, when compared to a simulation involving pseudo-random numbers. The disadvantages and/or issues involved are also examined.

Real-world currency calibration: modelling fixed exchange rates

2010-01-20T14:52:48Z

The optimal choice of exchange rate regime is among the perennially debated issues in international economics. Exchange rate flexibility leads to efficient outcomes in the presence of sticky prices . Friedman (1953) and Mundell (1961) contain a more thorough discussion of advantages of a floating exchange rate. However, we believe that there is no single exchange rate regime that is suitable to all economies at all times. Whatever regime is adopted, it must fit consistently into the overall framework of macroeconomic policy.

In our ESG models, we currently do not distinguish between floating and fixed exchange rates. Exchange rates are modelled assuming that Purchasing Power Parity (PPP) or Uncovered Interest Rate Parity (UIRP) holds. These models assume a freely floating exchange rate. This note has two purposes.

First, we outline a new model for fixed or managed exchange rates. In the latter case, the currency board has an established target zone. We illustrate how the exchange rate model works using the HKD/USD exchange rate as an example. The fixed exchange rate model is proposed by Hui and Fong (2007).

This model is currently not implemented in the ESG, contact Barrie & Hibbert if you are interested in this model. The second part of this paper discusses a number of alternative ways that can be used in the current set up of our ESG models to model a fixed exchange rate.

We illustrate how the fixed exchange rate model works with the HKD/USD as an example.

Real world inflation modelling Real average earnings model: Long-term calibration

2010-01-15T10:14:49Z

Specific inflation rates are a concern for any institution with liabilities linked to prices in a particular region or sector. Aggregated price indices can only ever proxy the inflation rates relevant to individual firms, which means that risk management can be improved by calibrating models to inflation indices that better represent the inflation rate relevant to liabilities faced by a firm. This note presents calibration parameters and simulation targets for modelling wage inflation rates in multiple economies. Note that these models are not currently part of our standard ESG calibration, but can be set up on a bespoke basis.

Real-world interest rate calibration: Constructing medium-term inflation forecasts

2010-01-13T16:07:58Z

This note describes a change to our real rate calibration methodology with regard to the inclusion of medium-term inflation forecasts for economies where no index-linked bonds are available. From the end-December 2009 calibration onwards, in the absence of index-linked government bonds, five- and ten-year econometric inflation forecasts will be incorporated into the calibration in addition to the one-year forecasts that we have traditionally included in our calibrations.

Quarterly financial markets update: Financial markets in 2009

2010-01-05T12:02:29Z

2009 has been a year of recovery and stabilisation in financial markets. Since the end of the first quarter the world’s major stock markets have enjoyed strong gains coupled with declining levels of implied volatility. Corporate credit spreads have fallen back in line with average post war levels and inflation expectations have been revised upwards as tentative signs of a global recovery have emerged, increasing the level and slope of risk-free yield curves.

Whilst it now appears that recovery is underway across the world’s major economies robust growth rates and asset returns are not certain for 2010 and beyond. There is a distinct lack of clarity over the impact of the policy initiatives undertaken by governments and central banks in late 2008 and through 2009.

This document contains a summary of key developments in financial markets for GBP, EUR, USD and JPY. A special issue is included on the performance of some of our Real-World calibrations over 2009.

Real-world equity calibration: Distributional targets at end-December 2009

2010-01-05T10:18:37Z

This note provides an update to our real-world volatility, correlation and risk premium assumptions for global equity markets at end-December 2009. In our view, the assumptions presented here provide a set of feasible real-world calibration targets. Please note that these targets may not be precisely matched by specific model calibrations. In general models offer fewer degrees of freedom than the number of targets documented here. As a result, the actual choice of the calibration targets used in the fitting process is described in the model calibration documentation.

Displaced Diffusion Libor Market Model

2010-01-05T09:59:04Z

The Barrie & Hibbert iESG allows users to model the term structure of nominal interest rates using the Libor Market Model (LMM) which gives great scope for accurate calibration to derivative prices as observed in the market. However, when using this model in a market-consistent framework it is possible to observe cases of extremely high interest rates (exploding rates), which some ESG users find undesirable.

The Displaced Diffusion Libor Market Model is a common extension to the standard lognormal Libor Market Model, where the forward rate distribution is shifted by some constant. In this paper we’ll show that if we choose the displacement carefully, DDLMM is actually exactly equivalent to the Gaussian case of the ubiquitous Heath Jarrow Morton model, in which all continuously compounded rates are normally distributed- giving us a model which allows for extremely accurate calibration while reducing (or indeed eliminating) the occurrence of exploding rates.