Modelling, Pricing, and Hedging Counterparty Credit Exposure | springerprofessional.de

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Modelling, Pricing, and Hedging Counterparty Credit Exposure

A Technical Guide

verfasst von: Giovanni Cesari, John Aquilina, Niels Charpillon, Zlatko Filipovic, Gordon Lee, Ion Manda

Verlag: Springer Berlin Heidelberg

Buchreihe : Springer Finance

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

It was the end of 2005 when our employer, a major European Investment Bank, gave our team the mandate to compute in an accurate way the counterparty credit exposure arising from exotic derivatives traded by the ?rm. As often happens, - posure of products such as, for example, exotic interest-rate, or credit derivatives were modelled under conservative assumptions and credit of?cers were struggling to assess the real risk. We started with a few models written on spreadsheets, t- lored to very speci?c instruments, and soon it became clear that a more systematic approach was needed. So we wrote some tools that could be used for some classes of relatively simple products. A couple of years later we are now in the process of building a system that will be used to trade and hedge counterparty credit ex- sure in an accurate way, for all types of derivative products in all asset classes. We had to overcome problems ranging from modelling in a consistent manner different products booked in different systems and building the appropriate architecture that would allow the computation and pricing of credit exposure for all types of pr- ucts, to ?nding the appropriate management structure across Business, Risk, and IT divisions of the ?rm. In this book we describe some of our experience in modelling counterparty credit exposure, computing credit valuation adjustments, determining appropriate hedges, and building a reliable system.

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Inhaltsverzeichnis

Frontmatter

Methodology

Frontmatter

Chapter 1. Introduction

Abstract

The aim of this first chapter is to introduce basic notions of counterparty credit exposure, and to motivate with a few simple examples the problems and concepts we will be considering in more detail later in this book.

Giovanni Cesari, John Aquilina, Niels Charpillon, Zlatko Filipović, Gordon Lee, Ion Manda

Chapter 2. Modelling Framework

Abstract

Our goal is to define a general framework which can be used to compute counterparty credit exposure for all types of transactions. As highlighted in the Introduction, computing counterparty exposure consists of computing distributions of prices at future times. For simple products this can be achieved by scenario simulation, followed by pricing on each scenario, at each time step. However, in the case where no analytical form is known for the price of the product, this approach is not practical and a different approach is required.

Giovanni Cesari, John Aquilina, Niels Charpillon, Zlatko Filipović, Gordon Lee, Ion Manda

Chapter 3. Simulation Models

Abstract

In Chap. 2 we defined a general framework to enable estimation of counterparty exposure for different product classes. Throughout, we highlighted the importance of being able to simulate price processes of different asset classes simultaneously and in consistent fashion. This was accomplished by simulating a martingale process for each asset class. By doing so, the models fit time-zero forward curves by construction, so that calibration involves only choosing the volatility structure for the martingale pertaining to each asset class.

In this chapter we focus on specific choices of models for different asset classes, discussing how they can be implemented and calibrated within our framework.

Giovanni Cesari, John Aquilina, Niels Charpillon, Zlatko Filipović, Gordon Lee, Ion Manda

Chapter 4. Valuation and Sensitivities

Abstract

Conceptually there are two steps in computing credit exposure: simulation followed by pricing. First, one needs to simulate scenarios from the distribution of the underlying processes that drive the price of the product concerned. Secondly, the price of this product needs to be evaluated at each time in the simulation schedule for each of the simulated scenarios.

Giovanni Cesari, John Aquilina, Niels Charpillon, Zlatko Filipović, Gordon Lee, Ion Manda

Architecture and Implementation

Frontmatter

Chapter 5. Computational Framework

Abstract

Our goal is now to show how this mathematical framework can be naturally translated into a computational framework that will enable the computation of exposure in a systematic way for all types of products across the asset classes we provided models for. The basic ideas we highlight in this chapter will lead to the description of a basic software architecture, which can be used to address typical integration problems that large financial institutions face. The motivation for many of the challenges we consider in this and the following chapters, as well as many of the choices we take, will become clearer in Part IV, where the computation, controlling, and hedging of exposure, will be done at counterparty and not just at trade level.

Giovanni Cesari, John Aquilina, Niels Charpillon, Zlatko Filipović, Gordon Lee, Ion Manda

Chapter 6. Implementation

Abstract

The previous chapter introduced a computational framework within which complicated payoffs can be specified and then simulated to obtain the price distributions required for credit exposure estimation. Trade specification is based on quantities we called statistics, which can be thought of as functions that return some financial quantity, given a simulated scenario. We will use these statistics later in Part III to specify various products.

This chapter is dedicated to a more detailed analysis of various statistics. We describe their implementation, the practical issues that arise, and the solutions we adopted. Since simulation is at the heart of our framework, we describe also various Monte Carlo schemes for simulating SDEs. We end the chapter by analysing the different types of errors introduced in the various steps of the modelling.

Giovanni Cesari, John Aquilina, Niels Charpillon, Zlatko Filipović, Gordon Lee, Ion Manda

Chapter 7. Architecture

Abstract

We have described how the AMC algorithm translates into a computational framework that allows systematic counterparty exposure computation of different products. The main result achieved so far is that, within this framework, products are described via their generic features and not their specific definition. This has provided the capability of using functions of financial quantities, which we have called statistics, to define products. As an additional step we have introduced a Portfolio Aggregation Language, PAL, to book trades in the system and, thus, use the analytics in a flexible way. As a result the concept of a new type of product, defined in terms of price distribution of other products, has been introduced. We have called these products super-products, with the most relevant example in this context being the Contingent Credit Default Swap (C-CDS).

Giovanni Cesari, John Aquilina, Niels Charpillon, Zlatko Filipović, Gordon Lee, Ion Manda

Products

Frontmatter

Chapter 8. Interest-Rate Products

Abstract

In Chap. 4 and 5 we described a generic valuation framework which takes into account the possibility of transactions having early exercise features. In the notation that we introduced there, we represent by T={τ ₁,τ ₂,…,τ _n}∪{∞} the set of times at which the holder of the option may opt to replace the no-exercise portfolio P with time-t value \(V_{t}^{P}\) , with a different portfolio Q with time-t value \(V_{t}^{Q}\) ({∞}=T ^∞ indicates no-exercise). The goal of this and of the next chapters is to compute counterparty credit exposure for different types of transactions.

Giovanni Cesari, John Aquilina, Niels Charpillon, Zlatko Filipović, Gordon Lee, Ion Manda

Chapter 9. Equity, Commodity, Inflation and FX Products

Abstract

In the previous chapter we considered some of the most common products traded in the interest-rate market. We now turn our attention to standard equity, commodity, foreign exchange and inflation products.

Giovanni Cesari, John Aquilina, Niels Charpillon, Zlatko Filipović, Gordon Lee, Ion Manda

Chapter 10. Credit Derivatives

Abstract

In this chapter we consider credit derivatives, focussing on loss products. In our framework single name CDSs are just a special case of multi-name CDOs, as the loss dynamics can be described in the same way for both product types. As, however, CDSs have specific features which can be used to introduce more general characteristics of other credit derivatives products, we consider first this type of products. We move then to the classical CDO tranches and show how credit exposure strongly depends on the seniority of the tranche.

Giovanni Cesari, John Aquilina, Niels Charpillon, Zlatko Filipović, Gordon Lee, Ion Manda

Chapter 11. Structures

Abstract

We consider now some structured products, which show interesting credit exposure characteristics. As we will see these examples are not necessarily complex to model. They are, however, interesting to examine, as they are commonly used in the industry, and they have features which may only appear in the context of credit exposure. In general, the complexity of these transactions is in the structure itself, and the challenge lies in understanding what to model, rather than how to model. We will give here only a brief overview of the products and of their structures, without entering into details.

Giovanni Cesari, John Aquilina, Niels Charpillon, Zlatko Filipović, Gordon Lee, Ion Manda

Hedging and Managing Counterparty Risk

Frontmatter

Chapter 12. Counterparty Risk Aggregation and Risk Mitigation

Abstract

In the previous chapters we have considered credit exposure of single transactions. We examine now how to aggregate these exposures at counterparty level and then how to control and manage the risk from a portfolio perspective. This is where the real challenge starts and where it becomes clear why a robust modelling framework is necessary. To obtain a portfolio view it is necessary in fact to calibrate models and to compute products of different nature in a consistent way. In a classical Monte Carlo framework, where exposure is computed in two distinct steps, i.e. first by generating scenarios and then by pricing (using analytical pricers or suitable approximations), this commonality is achieved by using the same consistent scenarios across products. In our framework where scenario generation and pricing are linked together, the scenario consistency is embedded in the underlying pricing model. The hybrid product we need to value taking into account all stochastic drivers in a consistent way, is the given portfolio of transactions.

Giovanni Cesari, John Aquilina, Niels Charpillon, Zlatko Filipović, Gordon Lee, Ion Manda

Chapter 13. Combining Market and Credit Risk

Abstract

The valuation approach detailed in Chap. 4 is centered on estimating the distribution of future values of a transaction after having simulated trajectories of the underlying stochastic drivers. When markets are complete, the pricing-by-arbitrage paradigm allows us to price stochastic payoffs as an expectation in a particular measure, namely the one under which the prices of assets are martingales when expressed in units of a chosen numeraire.

Giovanni Cesari, John Aquilina, Niels Charpillon, Zlatko Filipović, Gordon Lee, Ion Manda

Chapter 14. Pricing Counterparty Credit Risk

Abstract

We have analysed in the previous chapters the most straightforward ways of mitigating the risk of default of a counterparty, namely by imposing limits on transacted notional amounts and by negotiating collateral agreements with the counterparty.

A more flexible alternative is to buy protection or insurance on the given counterparty, typically in the form of a Credit Default Swap (CDS). In practice, however, risk mitigation via CDSs is not always straightforward.

Giovanni Cesari, John Aquilina, Niels Charpillon, Zlatko Filipović, Gordon Lee, Ion Manda

Backmatter

Titel: Modelling, Pricing, and Hedging Counterparty Credit Exposure
verfasst von: Giovanni Cesari
John Aquilina
Niels Charpillon
Zlatko Filipovic
Gordon Lee
Ion Manda
Copyright-Jahr: 2009
Verlag: Springer Berlin Heidelberg
Electronic ISBN: 978-3-642-04454-0
Print ISBN: 978-3-642-04453-3
DOI: https://doi.org/10.1007/978-3-642-04454-0

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