The first edition of Advanced Financial Risk Management was published eight years ago. My Kamakura colleagues and co-authors Kenji Imai and Mark Mesler and I were very pleased when our friends at John Wiley approached us about a dramatically revised second edition in light of the credit crisis. The revised book is now in the hands of the production crew at John Wiley, and we thought it would be helpful to give you a preview of the book well in advance of its forecast publication date. That forecast, by the way, is for April Fool’s Day, 2013.

What is different in the second edition? We’ve make a massive attempt to replace assumptions with facts and to be very blunt about which models worked and which didn’t work in light of the credit crisis events from 2006 to 2011. We’ve also moved mountains of data, including 50 years of daily U.S. Treasury yield curves, 22 years of daily default probabilities thanks to Kamakura Risk Information Services, almost 2 years of weekly credit default swap trading volumes from DTCC, and a year of daily borrowings from the Fed by hundreds of banks during the credit crisis.

The facts are quite clear in light of the credit crisis. The core integrated risk measure, the Jarrow-Merton value of the put option on the firm, is still the best indicator of the overall integrated risk of a financial institution. In order to calculate that put option value, when it’s not observable in the market for put options, we should be using the best models available in light of the evidence of the last few years. We’ve made a lot of changes in the book in order to do that:

1. We’ve replaced one factor interest rate models with a series of Heath Jarrow and Morton interest rate models. We use a 3 factor implementation of the HJM approach for most of the worked valuation examples. We note that BIS market risk rules require at least 6 factors for accuracy and we agree with that conclusion. Our colleague Robert Jarrow tells us that the worked examples of 2 factor and 3 factor HJM “bushy trees” are the first that he has seen in the literature.

2. We’ve increased the role of reduced form credit models throughout the book because the performance of the models through the crisis was exceptionally good. You’ll see lots of screen prints and test results from KRIS version 5 default models. You’ll also see lots of “pseudo code” for how to use the reduced form approach to model complex balance sheets and portfolios.

3. We share the conclusions of a bi-partisan report from the U.S. Senate that the rating agencies failed miserably in the credit crisis. We label credit ratings a “legacy” tool and relegate ratings to second tier status.

4. We do the same with Merton model default probabilities. John Campbell, Jens Hilscher and Jan Szilagyi’s 2011 paper in the *Journal of Investment Management *won the Markowitz Award for best paper in part for their conclusions that reduced form default probabilities substantially outperformed Merton default probabilities. Prof. Merton himself was one of the four Nobel prize winners who selected the Markowitz prize winner, so we feel very comfortable applying the legacy label to Merton default probabilities as well. For similar reasons, we’ve moved the discussion of the copula method for CDO valuation to our “credit risk museum.”

5. We’ve used lots of yield curve data to report on the nature of yield curve movements and to guide us as to which term structure modeling approaches work best.

6. We’ve used Fed borrowing data in the credit crisis to report on the five largest borrowers during the credit crisis.

7. Since a multi-factor approach to yield curve modeling is essential for realism, we’ve emphasized bushy trees and Monte Carlo solutions to fixed income valuation problems, replacing many of the mathematical formulas that were obtainable (usually) only with one risk factor driving interest rates.

We are very pleased to share selected chapters of the book with clients of Kamakura and friends of the firm. We’ve listed a synopsis of each chapter below. Please contact us at info@kamakuraco.com if you would like an advanced copy of a few key chapters.

**Advanced Financial Risk Management:
Second Edition**

**Tools and Techniques for Integrated Credit Risk, Market Risk, Liquidity Risk and Interest Rate Risk Management**

**April 2012
Donald R. van Deventer
Kenji Imai
Mark Mesler**

Introduction and the Wall Street Lessons from Bubbles

Abstract

The introduction highlights six key risk management fallacies that were very important in worsening the 2006-2011 credit crisis. We include a detailed chronology of the credit crisis to illustrate those fallacies.

Key terms

Credit crisis, risk management fallacies, credit crisis chronology, Lehman Brothers, Bear Stearns

**Part 1: Risk Management: Definitions and Objectives**

**Chapter 1: A risk management synthesis: Market risk, credit risk, liquidity risk and asset and liability management**

Abstract

This chapter starts with the long-running battle between mark to market and net income-simulation based risk management. Key quotes from the credit crisis summarize the reasons for failure of the “too big to fail” firms. We state the objectives of risk management. We explain important milestones in the advancement of the risk management discipline.

Key terms

Risk management objectives, home prices, net income simulation, mark to market

**Chapter 2: Risk, return, performance management, and capital regulation**

Abstract

This chapter is focused on risk, return, performance measurement and capital regulation. We discuss the impact of selection bias in many forms of performance measurement, including historical value at risk and tracking error versus an index. We discuss transfer pricing and its development in the banking industry and close with a discussion of capital regulation in the financial services business.

Key terms

Risk, return, performance measurement, selection bias, capital regulation, transfer pricing

**Part 2: Risk Management Techniques for Interest Rate Analytics**

**Chapter 3: Interest rate risk introduction and overview**

Abstract

This chapter argues that interest rate risk cannot be studied without learning from history. We review 50 years of daily U.S. Treasury yield curve movements. We discuss the Jarrow-Merton put option as the best single measure of total risk. We discuss the interest rate risk “safety zone.”

Key terms

U.S. Treasury, yield curve, put option, interest rate risk, safety zone

**Chapter 4: Fixed income mathematics, the basic tools**

Abstract

This chapter introduces basic fixed income mathematics, including the concepts of present value, zero coupon bond prices, and forward interest rates. It discusses the many assumptions embedded in the yield to maturity concept.

Key terms

Forward rate, present value, zero coupon, bond price, yield to maturity

**Chapter 5: Yield curve smoothing**

Abstract

This chapter derives four different methods for yield curve smoothing and concludes that the maximum smoothness forward rate method is the most robust. It discusses the fatal flaws of the Nelson-Siegel smoothing approach. We conclude with a discussion of the Shimko test for choosing among smoothing methods.

Key terms

Maximum smoothness, forward rates, cubic spline, Nelson-Siegel, Shimko test

**Chapter 6: Introduction to Heath, Jarrow and Morton interest rate modeling**

Abstract

This chapter introduces Heath Jarrow and Morton interest rate simulation using a one factor model and a bushy tree. We derive the no arbitrage version of the bushy tree and demonstrate risk neutral valuation techniques.

Key terms

HJM, Robert Jarrow, risk neutral, valuation, digital option

**Chapter 7: HJM interest rate modeling with rate and maturity-dependent volatility**

Abstract

This chapter generalizes the HJM bushy tree approach of Chapter 6 by introducing interest rate volatility that is dependent on both maturity of the forward rate and on rate levels. We provide a worked example of no arbitrage risk-neutral valuation of zero coupon bonds, coupon bearing bonds, and a digital interest rate option.

Key terms

HJM, risk neutral, interest rate volatility, valuation, digital option, 1 factor

**Chapter 8: HJM interest rate modeling with 2 factors**

Abstract

This chapter explains why the prevalence of yield curve twists in market yield movements renders single factor term structure models inaccurate. We introduce a two factor HJM model and construct the bushy tree for valuation of zero coupon bonds, coupon-bearing bonds, and digital interest rate options.

Key terms

HJM, two factor, bushy tree, risk neutral, interest rate volatility

**Chapter 9: HJM interest rate modeling with 3 Factors**

Abstract

This chapter shows how to test whether additional interest rate risk factors are necessary for increased accuracy in interest rate modeling. We construct a worked example of an HJM three factor model bushy tree and demonstrate no arbitrage risk neutral valuation.

Key terms

HJM, three factors, bushy tree, risk neutral, interest rate volatility

**Chapter 10: Valuation, liquidity, and net income simulation**

Abstract

This chapter shows why not even a three factor interest rate model is sufficient to accurately model interest rate movements. It discusses the Basel market risk requirement that banks use at least six risk factors to drive interest rates. We discuss Monte Carlo simulation in the Heath Jarrow and Morton framework. We outline common pitfalls in the practical simulation of interest rate risk using Monte Carlo simulation.

Key terms

Valuation, liquidity, net income simulation, empirical probabilities, risk neutral probabilities, Monte Carlo simulation, BIS, market risk

**Chapter 11: Interest rate risk mismatching and hedging**

Abstract

In this chapter we re-introduce the concept of the safety zone and discuss the institutional constraints on interest rate risk mismatching and hedging.

Key terms

Interest rate risk, mismatching, hedging, insurance, pensions, banking

**Chapter 12: Legacy approaches to interest rate risk management**

Abstract

In this chapter we discuss legacy interest rate risk tools like gap analysis, duration, and convexity. We discuss the errors that emerge from duration hedging when more than one factor is driving interest movements. We again discuss the interest rate safety zone since, inside the zone, no interest rate risk hedging creates shareholder value.

Key terms

Duration, convexity, gap analysis, safety zone, interest rate risk

**Chapter 13: Special Cases of Heath, Jarrow and Morton**

Abstract

In this chapter we discuss special cases of the HJM term structure modeling approach. We explore duration as a term structure model and then derive the Ho and Lee, Vasicek and Hull and White “Extended Vasicek” models.

Key terms

Term structure model, Ito’s lemma, no arbitrage, duration, Merton model, Ho and Lee model, Vasicek model, Hull-White model

**Chapter 14: Estimating the parameters of interest rate models**

Abstract

In this chapter we expand the definition of no arbitrage to include all fixed income instruments with observable prices and valuation dependent on the base yield curve. We use the example of callable bonds to demonstrate how to imply interest rate volatility from observable security values.

Key terms

Implied volatility, interest rate volatility, no arbitrage, callable bond, European call

**Part 3: Risk Management Techniques for Credit Risk Analytics**

**Chapter 15: An introduction to credit risk: Using market signals in loan pricing and performance measurement**

Abstract

In this chapter, we discuss the use of market data for credit risk management. We review the market concentration of the credit default swap market and the lack of non-dealer trading volume. We conclude that CDS data is not of sufficient robustness to provide a solid foundation for credit risk analysis.

Key terms

Credit risk, credit default swap, trading volume, DTCC

**Chapter 16: Reduced form credit models and credit model testing**

Abstract

This chapter begins with the history of reduced form credit models originally developed by Robert Jarrow and Stuart Turnbull. We introduce the theory of reduced form models and their application to zero coupon bond pricing for risky issuers. We discuss fitting reduced form models to observable securities prices and historical default data bases. We use examples from Kamakura Risk Information Services to illustrate reduced form model results from the credit crisis. We conclude the chapter with an extensive reviewing of credit modeling testing.

Key terms

Reduced form, probability of default, model testing, logistic regression, credit model, credit default swaps

**Chapter 17: Credit spread fitting and modeling**

Abstract

In Chapter 17 we show how to apply the maximum smoothness forward rate smoothing approach of Chapter 5 to the credit spreads of a bond issuer who may default. We discuss problems with the conventional quotation of credit spreads. We illustrate how to extract yield curves from coupon bearing bond prices. We illustrate the pitfalls of smoothing curves with credit risk while ignoring the risk free curve. We discuss problems associated with the manipulation of Libor and the risks of similar manipulation of credit default swap pricing. We close with a discussion of the factors that determine the magnitude of credit spreads.

Key terms

Credit spread, credit risk, default probability, maximum smoothness, Libor, credit default swaps

**Chapter 18: Legacy Approaches to credit risk
**

Abstract

In this chapter we review legacy approaches to credit risk measurement that have been outperformed by the reduced form approach to credit risk. We start with traditional credit ratings and point out the lack of accuracy in rating agency self-assessment of their own performance. We summarize the conclusions of the U.S. Senate on performance of the rating agencies in the credit crisis. We also compare the accuracy of ratings and reduced form models in predicting default, finding a wide advantage for reduced form models. We close the chapter by reviewing the 40 year old Merton model of risky debt and explain the results of modern research, which finds the Merton approach to be much less accurate than reduced form models.

Key terms

Credit ratings, rating agency, transition matrix, ratings accuracy, ratings problems, Merton model, Merton default probabilities

**Part 4: Risk Management Applications, Instrument by Instrument**

**Chapter 19: Valuing credit risky bonds**

Abstract

In this chapter we use the 3 factor Heath Jarrow and Morton bushy tree from Chapter 9 to value various types of bonds for both risk-free and risky issuers: zero coupon bonds, bullet bonds, amortizing bonds and floating rate bonds. We discuss the difference in analysis for defaultable bonds versus risk free bonds at length.

Key terms

HJM, bushy tree, credit risk, floating rate bond, fixed rate bond, amortizing bond

**Chapter 20: Credit derivatives and collateralized debt obligations**

Abstract

This chapter outlines the reduced form approach to the valuation of credit default swaps and collateralized debt obligations. We review again the lack of trading volume in single name credit default swaps. We outline step by step procedures for the valuation of any complex credit portfolio, with specific applications to CDOs. We provide a worked example showing how default probabilities that are dependent on common macro-economic factors have a logical and explicit correlation. Finally, we summarize the flaws in the copula approach to CDO valuation that is widely cited as a contributor to massive losses in CDOs.

Key terms

Reduced form, credit model, credit default swap, collateralized debt obligation, copula method, correlated default

**Chapter 21: European options on bonds**

Abstract

This chapter uses the 3 factor HJM bushy tree from Chapter 9 to value put and call options on a coupon-bearing bond. We also value a bond with a European option to call the bond. We discuss extension of the analysis to options on the bonds of a risky issuer.

Key terms

HJM, 3 factors, bond options, call options, put options, callable bond

**Chapter 22: Forward and futures contracts**

Abstract

In this chapter we use the 3 factor HJM bushy tree from Chapter 9 to value a series of futures and forward contracts. We start with forward contracts on zero coupon bonds, then value forward rate agreements and Eurodollar and Sydney bank bill futures contracts.

Key terms

HJM, bushy tree, 3 factors, futures contract, forward contract, bond futures, Eurodollar futures, forward rate agreements

**Chapter 23: European options on forward and futures contracts**

Abstract

Chapter 23 applies the 3 factor HJM bushy tree to value European call and put options on zero coupon bond forwards, forward rate agreements, and Eurodollar futures contracts.

Key terms

HJM, 3 factor, bushy tree, call option, put option, forward contracts, forward rate agreements, money market futures

**Chapter 24: Caps and floors**

Abstract

This chapter begins with a discussion of the 2012 revelation that Libor had been manipulated by Libor panel banks beginning in 2005. Assuming the reference rate is not manipulated, we use the 3 factor HJM bushy tree in Chapter 9 to value interest rate caps and floors. We then value a floating rate loan with an embedded cap. We follow that with the valuation of a loan with both caps and floors on its floating rate.

Key terms

Libor, caps, floors, HJM, 3 factor, bushy tree, manipulation

**Chapter 25: Interest rate swaps and swaptions**

Abstract

Chapter 25 employs the 3 factor HJM bushy tree of Chapter 9 to value the fixed side of an interest rate swap, the floating side of an interest rate swap, and the combined swap position. We discuss valuation of swaptions using the same approach and the implications of counterparty default for valuation.

Key terms

Interest rate swap, swaptions, HJM, 3 factor, bushy tree

**Chapter 26: Exotic swap and option structures**

Abstract

The 3 factor HJM bushy tree from Chapter 9 is used in this chapter to demonstrate the risk neutral valuation of almost any type of interest rate derivative. We discuss arrears swaps, digital interest rate options, digital range floaters and other exotic structures.

Key terms

HJM, 3 factor, bushy tree, digital option, arrears swap, digital range notes

**Chapter 27: American fixed-income options**

Abstract

Chapter 9’s 3 factor HJM bushy tree is used again in this chapter, this time to value a bond with an embedded American call option. Next, we discuss alternative methods for valuing American call options, including Monte Carlo simulation, binomial lattices, trinomial lattices, and the finite difference method.

Key terms

HJM, 3 factor, bushy tree, American option, callable bond valuation

**Chapter 28: Irrational exercise of fixed income options**

Abstract

This chapter focuses on the valuation of an amortizing loan with an embedded American call option. We first use the HJM 3 factor bushy tree from Chapter 9 to value the loan on the assumption that it will be called in a rational way. In the second case, we assume that the call option is exercised “irrationally” and we introduce the concept of transactions costs that may be a real barrier to the rational exercise of the call option.

Key terms

HJM, 3 factor, bushy tree, American call option, amortizing loan, irrational exercise of options, transactions costs

**Chapter 29: Mortgage-backed securities**

Abstract

We begin this chapter with a review of the legacy approaches to valuing mortgage-backed securities and asset-backed securities. We then discuss a more modern approach where logistic regression or multinomial logit are used to model the probability of prepayment and default as a function of home prices, the interest rate environment and other factors. We then discuss key issues in the valuation of mortgage servicing rights.

Key terms

Mortgage-backed securities, asset-backed securities, prepayment, default, logistic regression, multinomial logit, mortgage servicing rights

**Chapter 30: Non-maturity deposits**

Abstract

In this chapter, we value non-maturity deposits using the HJM 3 factor bushy tree from Chapter 9 in two ways. First, we value deposits as if the credit risk of the bank has no impact on deposit balances. After reviewing the deposit run-off of Wachovia prior to its failure in 2008, we value deposits on the assumption that credit risk triggered by high interest rates will trigger a major deposit run-off. We close with a study of German 3 month notice deposits.

Key terms

Deposit valuation, non-maturity deposits, credit risk, HJM, 3 factor, bushy tree, Wachovia

**Chapter 31: Foreign exchange markets: a term structure model approach**

Abstract

In this chapter, we follow Amin and Jarrow in a discussion about how to model foreign exchange derivatives using the HJM approach. For historical perspective, we also review legacy foreign currency options formulas in two cases: when interest rates are constant and when interest rates in the two countries follow a one-factor Vasicek term structure model.

Key terms

HJM, foreign currency option, Vasicek model

**Chapter 32: Impact of collateral on valuation models: the example of home prices in the credit crisis**

Abstract

This chapter uses the credit crisis experience of collapsing home prices and subsequent mortgage defaults. We show, using the HJM 3 factor bushy tree from Chapter 9, how to incorporate the random movements of home prices into default and prepayment experience and mortgage valuation.

Key terms

HJM, 3 factor, bushy tree, home prices, Case-Shiller, collateral values, default, prepayment

**Chapter 33: Pricing and valuing revolving credit and other facilities**

Abstract

This chapter uses the credit crisis experience of Countrywide Financial and Royal Bank of Scotland in a discussion about the valuation of revolving lines of credit. Balances on revolvers are driven by both normal seasonality in cash flow needs and credit-event driven needs. A complete approach to valuation incorporates both elements.

Key terms

Royal Bank of Scotland, Countrywide Financial, revolving line of credit, put option on loan

**Chapter 34: Modeling common stock and convertible bonds on a default-adjusted basis**

Abstract

This chapter discusses the valuation of common stock and convertible bonds in a modern reduced form framework that recognizes the probability of default of the issuer. We use the example of Citigroup in our discussions. The framework follows the Amin and Jarrow framework discussed in Chapter 32 on the value of collateral.

Key terms

Common stock, convertible bonds, probability of default, reduced form, Citigroup

**Chapter 35: Valuing insurance policies and pension obligations**

Abstract

This chapter takes advantage of the common mathematical tool used in both life insurance valuation and credit risk analytics, the Cox process. We discuss the reduced form approach for valuing insurance liabilities of all major types.

Key terms

Life insurance, property and casualty insurance, valuation, Cox process

**Part 5: Portfolio Strategy and Risk Management**

**Chapter 36: Value at risk and Risk management objectives revisited at the portfolio and company level**

Abstract

This chapter is the central chapter of this book, focusing on risk management objectives at the institutional level. We discuss the Jarrow-Merton put option as the best single measure of total risk. We use the example of put options on the common stock of Citigroup to determine how much additional capital Citigroup would need for 100% certainty that Citigroup common stock would never fall below a given level. We pose four key pass-fail questions for management. We supplement that risk management test with 26 more questions that a sophisticated management team should be able to answer. We end by discussing the weaknesses of the value at risk approach, which is at the core of the conventional wisdom of bank capital adequacy. We show why there are dramatic differences in the VAR versus put option approach.

Key terms

Jarrow-Merton put option, common stock, Citigroup, value at risk

**Chapter 37: Liquidity analysis and management: examples from the credit crisis**

Abstract

This chapter focuses on the funding shortfalls of the five largest borrowers from the Federal Reserve during the credit crisis: AIG, the consolidated JPMorgan Chase-Bear Stearns-Washington Mutual, State Street, Morgan Stanley, and Dexia. We discuss the Jarrow-Merton put option as the best measure of liquidity risk.

Key terms

Liquidity risk, funding shortfall, Federal Reserve, put option, AIG, JP Morgan, State Street, Morgan Stanley, Dexia

**Chapter 38: Performance measurement: Plus alpha vs. transfer pricing**

Abstract

This chapter contrasts the “plus alpha” performance versus an index with transfer pricing and related financial accounting measures of performance used in commercial banking. We give a worked example of performance attribution on a fixed income portfolio. We discuss the critical role of default risk in the management of equity portfolios. We discuss the Jarrow-Merton put option concept as a tool for capital allocation as well.

Key terms

Performance measurement, plus alpha, transfer pricing, capital allocation, performance attribution, default risk, equity portfolios, put option

**Chapter 39: Managing institutional default risk and “safety and soundness”**

Abstract

This chapter applies the default risk questions for management that were listed in Chapter 36 to manage the default risk of the institution itself. We discuss at length why ratings and credit default swap quotes are flawed indicators of institutional credit risk. We use the default probabilities for Citigroup, Bank of America, Wells Fargo, Royal Bank of Scotland, and HBOS in discussing how to manage default risk.

Key terms

Default probability, credit ratings, credit default swaps, Citigroup, Bank of America, Wells Fargo, Royal Bank of Scotland, HBOS

**Chapter 40: Information technology considerations**

Abstract

This chapter discusses the demise of legacy “silo” risk systems and outlines the process by which leading financial institutions replace them with a modern integrated enterprise risk system. It discusses the request for proposal process, the pros and cons of a pilot installation, and how to be a “best practice” user of a sophisticated enterprise risk system.

Key terms

Enterprise risk, legacy system, silo risk, request for proposal, integrated risk

**Chapter 41: Shareholder value creation and destruction**

Abstract

This chapter concludes the book with a 10 point questionnaire that measures the institution’s existing primary risk system. The grade on this questionnaire is a very good indicator of the need for a system upgrade. We conclude with advice to senior management, middle management, and the working level on how to advance the firm’s state of the art in risk management.

Key terms

Risk system, integrated risk, default risk, stress test

Donald R. van Deventer

Kamakura Corporation

Honolulu, October 23, 2012

© Donald R. van Deventer, 2012. All rights reserved