Last update: July 29, 2001

References for Finance Engineering - Risk Management

Alexander, Carol et al. :
- Risk Management and Analysis, 1998, vol. 1 & 2.
Bessis, Joel :
- Risk Management in Banking, 1998.
Brockhaus, Oliver et al. :
- Equity Derivatives and Market Risk Models, 2000.
- Modelling and Hedging Equity Derivatives, 1999.

BibTeX references

Web links :

Risk Management and Analysis

Alexander, Carol (ed.)
John Wiley & Sons
Wiley Series in Financial Engineering
Volume 1: Measuring and Modelling Financial Risk, 1998.
Volume 2: New Markets and Products, 1998.

Risk Management in Banking

Joel Bessis
John Wiley & Sons, 1998, 574 pages.
496 pages 2nd edition (February 2001)

Introduction

PART I RISK MANAGEMENT

Risks
1. The Environment and the Evolution of Risks
2. Banking Risks
3. Credit Risk
4. Liquidity Risk
5. Interest Rate Risk
6. Market Risk
7. Foreign Exchange Risk
8. Solvency Risk
9. Operational Risk
Profitability
1. The Balance Sheet and Banking Transactions
2. The Income Statement and the Margins
3. Mark-to-Market Measures of Performance
4. Risk-adjusted Performance
Risk Management
1. The Roles of Risk Management
2. The Risk Management Process
3. Quantitative Risk Management: VAR and CAR
4. The Organization of Risk Management
Banking Regulations
1. Regulatory Issues
2. Capital Adequacy
3. The Current Capital Regulation
PART II MEASURING RISKS
Risk Measurement
1. Measuring Uncertainty
2. Sensitivity
3. Volatility
4. Unexpected Loss and VAR
5. Appendix 1: Calculation of Means and Standard Deviations
VAR
1. VAR, CAR and Risk Management
2. VAR and Common Indicators of Risks
3. Potential Loss
4. The Measurement of Unexpected Loss
5. Issues in Measuring VAR
PART III CREDIT RISK
Credit Risk
1. Credit Risk
2. Credit Risk Management
Credit Risk for Banking Transactions
1. Default Risk
2. Exposure Risk
3. Recovery Risk
4. Credit Risk and Potential Losses
5. Appendix 1: Default Probabilities over Varying Horizons
6. Appendix 2: The Term Structure of Default Risk
7. Appendix 3: Default Rates and Transition Matrices
Credit Risk for Market Instruments
1. Credit Risk for Market Instruments
2. Credit Risk for Derivatives
3. Implementation
4. Credit Risk Exposure for Portfolios of Derivatives
PART IV LIQUIDITY AND INTEREST RATE RISKS
The Liquidity Gap
1. The Liquidity Gap
2. Cash Matching
3. Liquidity Management
4. Issues for Determining the Liquidity Gap Time Profile
The Term Structure of Interest Rates
1. Interest Rates
2. The Term Structure of Interest Rates
3. Interest Rate Expectations
4. Liquidity and Costs of Liquidity
Interest Rate Gaps
1. The Interest Rate Gap
2. Marginal Interest Rate Gaps
3. The Risk-Reward Trade-off for Interest Rate Risk
4. Controlling Interest Rate Risk
The Limitations of Interest Rate Gaps
1. Determining Interest Rate Gaps
2. Interest Rate Gaps and Interest Indexes
3. Marginal Gaps and Intermediate Flows
Simulations
1. The Framework of Simulations
2. The Interest Rate Scenarios
3. Balance Sheet Projections
4. Projected Gap Profiles
5. Interest Margin Projections
6. Interest Rate Policy
7. Multiple Scenario Analysis with Business and Interest Rate Risks
8. The Simulations
9. Risk-Return Combinations
10. Simulations and Information
PART V MARK-TO-MARKET VALUE MANAGEMENT
Market Values
1. The Discount Rates
2. NPV and Margins for a "Bank Without Capital"
3. Discounted Margins and NPV with Capital
4. NPV and the Market Value of Equity
5. Appendix: NPV and Discounted Margins
Market Values and Interest Rate Risk
1. The Sensitivity of Market Values and Duration
2. Immunization of the Interest Margin
3. The Duration Gap and the Targets of Interest Rate Policy
4. The VAR Derived from the NPV
5. Appendix: The Immunization of the Net Margin over a Period
PART VI QUANTITATIVE CAPITAL MANAGEMENT
Capital Requirements
1. The Required Profitability on Capital
2. Profitability Targets
3. Quantitative Constraints Generated by Regulatory Capital
Securitization and Capital Management
1. The Mechanism of Securitization
2. The Analysis of a Securitization Transaction
3. Securitization and the Return on Equity
PART VII RISK-BASED CAPITAL
CAR
1. The Limitations of Simple Approaches to CAR
2. The Measure of Economic Capital
3. Economic Capital and Solvency
4. Choice of a Horizon for the Measure of Capital
Measuring CAR
1. Credit Risk
2. Market Risk
3. Interest Rate Risk
4. Aggregating Risks over Portfolios
Risk-adjusted Performance
1. Profitability Measures
2. Calculation of RAROC and SVA for Credit Risk
3. Risk-based Pricing
4. RAROC and Market Risk
5. The Price of Risk
PART VIII PORTFOLIO CREDIT AND MARKET RISKS
The Risk of Portfolios
1. Measuring Risk Diversification
2. Standalone Risk and Risk Contribution
3. Risk Allocation and Management
Correlations and Portfolio Risk
1. Risks and Correlations
2. Correlation and Covariance
3. The Implementation of Correlations
Credit Risk of Portfolios
1. Standalone Risk and Portfolio Risk
2. Default Statistics and Portfolio Losses
3. Portfolio Loss with Diversified Risks
4. The Correlation Methodology and the Portfolio Credit Risk
5. From Individual Risks to Portfolio Losses
6. Appendix: The Correlation Methodology
Market Risk of Portfolios
1. Correlations between Market Parameters and their Implications
2. The Volatility of the Portfolio Value
3. The Correlation Methodology
4. Interest Rate Exposures
5. The Multiple Simulations Methodology
PART IX FUNDS TRANSFER PRICING AND CAPITAL ALLOCATION
Funds Transfer Pricing Systems
1. The Internal Management of Funds and Netting
2. The Commercial and the Financial Margins
3. Transfer Prices and Policy
Economic Transfer Prices
1. Setting Target Margins
2. From Transfer Prices to Customer Prices
3. The Cost of Funds for Assets
4. The Separation of Commercial and Financial Risks
PART X PORTFOLIO MANAGEMENT
The Management of Banking Portfolios
1. The Allocation of Capital
2. Risk-adjusted Performance
3. RAROC and Risk Pricing
4. Portfolio Management
5. Appendix: Quantitative Portfolio Management
PART XI IMPLICIT OPTIONS IN BANKING PRODUCTS
Embedded Options
1. Optional Risk: Two Examples
2. Modelling Prepayments
3. Gains and Losses from the Prepayment Option
The Value of Embedded Options
1. The Valuation of Options
2. Generating Simulated Interest Rates
3. The Valuation of the Prepayment Option
4. The Option Adjusted Spread (OAS)
Convexity Risks
1. The Market Value of the Balance Sheet and the Interest Rates
2. Duration and Convexity
3. The Sensitivity of NPV
4. The Impact of Embedded Options on the NPV
5. Controlling the Risk of NPV

Bibliography

Equity Derivatives and Market Risk Models

By Oliver Brockhaus, Michael Farkas, Andrew Ferraris, Douglas Long, and Marcus Overhaus, Deutsche Bank, UK.

Risk Books publ., London, UK, January 2000.

The Black-Scholes Framework
1. The Black-Scholes equity model
2. Extensions to Black-Scholes
Skew Models
1. Introduction
2. Volatility surface generation
3. Volatility smile model
4. Volatility surface dynamics
Jump Diffusion Models
1. Model description
2. Options pricing
3. Fitting the smile
Deterministic Volatility Models
1. Introduction
2. Calibration techniques
3. Hedging
Stochastic Volatility Models
1. The Hull-White model
2. The Heston model
3. Calibration
4. Hedging
5. Introduction to Arch and Garch
Credit Spread Models
1. Merton's model
2. Structural models
3. Intensity models
4. Convertible bonds with credit risk
Trees
1. Thick tree
2. Implied trees
3. Stochastic trees
4. Generic tree framework
Finite Difference
1. One-dimensional techniques
2. Path-dependent options
3. Two-dimensional techniques
4. Generic finite difference
Monte Carlo
1. Local volatility in Monte Carlo
2. Ito-Taylor expansion
3. Greeks in Monte Carlo
4. Generic Monte Carlo framework
Alternative Approaches
1. Fourier transforms
2. Laplace transforms
3. Path integral
American Options on Multi-assets
1. Markov chain method
2. Regression for continuation value
3. Simulated tree
4. Stochastic mesh
Volatility Contracts
1. Variance swaps
2. Covariance swaps
3. Volatility swaps
4. Volatility options
Discrete Sampling Options
1. Barriers
2. Lookbacks
Additional Products
1. Cliquet with smile - analytical approximation
2. Barrier options with a smile
3. Passport options
Introduction to Risk Management
1. Market risk
2. Credit risk
3. Raroc
Value-at-Risk
1. The VaR approach
2. VaR methodologies
3. Simulated VaR
4. Analytical VaR
5. Correlation concepts
Extreme Value Theory
1. The domain of attraction
2. A central limit theorem for maxima
3. Point process approach
4. Estimation of the tail distribution
5. A limit theorem for the excess distribution
6. The peaks over threshold (POT) method
7. Dynamic extreme value theory
8. Multi-day returns
9. Multivariate EVT
10. Hill estimation
Coherent Risk Measures
1. Axioms for acceptance sets
2. Correspondence between acceptance sets and risk measures
3. Axioms for risk measures
4. Correspondence between the axioms on acceptance sets and risk measures
5. Value-at-risk and expected shortfall
6. Model-free risk measures
7. Generalised scenarios
Credit Risk Management
1. The asset value model
2. The credit quality migration model
3. CreditRisk+

Modelling and Hedging Equity Derivatives

By Oliver Brockhaus, Andrew Ferraris, Christoph Gallus, Douglas Long, Reiner Martin, Marcus Overhaus

Risk Books, publ., London, UK, June 1999.

Reviewed by Glyn Holton, Contingency Analysis :

This is an extraordinarily good book on equity option pricing. Written by a team of six Deutsche Bank financial engineers, it is targeted specifically toward financial engineers in the equity markets. It is highly practical and mathematically sophisticated. The core of the book is its explanations of how to price a wide variety of OTC equity derivatives, including exotics and derivatives that combine an equity component with either a fixed income or foreign exchange component. However, the book is far more than this. It opens with a sophisticated discussion of the financial mathematics that underlies financial engineering.

Depending upon the readers own knowledge, this can be used in either one of two ways. For readers who are familiar with measure-theoretic probability and stochastic calculus, it is a handy reference detailing important definitions and theorems. For less knowledgeable readers, it is an excellent road map for studying such advanced material. It clearly lays out important concepts, motivating what you need to learn if you read such standard texts as Baxter and Rennie, Breiman or Oksendal. Next, there are four chapters detailing closed form solutions for pricing everything from vanilla instruments to multi-asset and hybrid products. Three chapters cover quantitative methods based upon trees, Monte Carlo simulation and differential equations respectively. Other chapters cover volatility smiles, hedging, transaction costs and the development of pricing libraries.

Anyone who is or wants to be a financial engineer in the equity markets needs to read this book. The mathematical discussions are sophisticated, but they are also extremely practical and insightful. For example, the explanation of how to construct Sobol numbers is the best I have ever read. Also, market conventions and other useful information is provided as needed.

Comparison with other texts:

Haug is more of a reference. It details pricing formulas, but with little additional explanation. For end users who don't need to understand the theory, Haug is probably the better book. However, for financial engineers, Haug is no substitute.

The book is broader than Willmott, Dewynne and Howison, which focuses primarily upon pricing methods based upon differential equations. However, the explanations of how to price with differential equations are far more detailed in that book. Ultimately, financial engineers will need to read both books. Because it assumes less knowledge of mathematics, Willmott, Dewynne and Howison should be read first.

Mathematical Fundamentals
1. A Review of Probability Theory and Stochastic Calculus
2. The Black-Scholes Equity Model
3. Extensions to Black-Scholes
4. The Clark Formula
5. The Hybrid Model
6. The Multi-Currency Hybrid Model
Closed-Form Solutions for Standard Products
1. Basic Products
2. American Options
3. Digital Options
4. Barrier Options
5. Asian Options
Closed-Form Solutions for Non-Standard Products
1. Lookback Options
2. Fade-In Options
3. Fade-In Barrier Options
4. Chooser Options
5. Prolongation Options
6. Improving Options
7. Power and Powered Options
8. Compound Options
Closed-Form Solutions for Multi-Asset Products
1. Exchange Options
2. Relative Digital Options
3. Relative Outperformance Options
4. Outperformance options
5. European Digital Option on Best or Worst of Two Assets
6. Best or Worst of Several Assets
7. Basket Options
8. Hindsight Options
9. Outside Barrier Options
10. Outside Digital Options
Closed-Form Fixed Income and Hybrid Products
1. Bond Options and Swaptions
2. Caps and Floors
3. European Options (Merton Formula)
4. Equity/Bond Outperformance Options
The Tree Approach
1. Setting up the Tree
2. Option Pricing Using Trees
3. Barrier Options
4. Bermudan Asian Options
5. Convertible Bonds
Monte Carlo Methods
1. The Basic Method
2. Speeding Up Monte Carlo
3. Generic Monte Carlo Pricing
4. Hybrid Monte Carlo
5. Monte Carlo for American Options
A Partial Differential Equation Solver
1. Discretisation of the PDE
2. Boundary Conditions
3. Moving Barriers
4. Range and Fade-In Options
5. American Options
6. Discrete Dividends
7. Model Calibration
Further Modelling Issues
1. Calibration of the Extended Vasicek Model
2. Basket and Asian Underlyings
3. Volatility Smile
Hedging
1. Hedging and Risk Management
2. Pricing and Hedging European Options Under Transaction Costs
3. Hedging of Specific Products
Implementation Issues
1. The Context of a Model Library
2. Library Interface Design
3. Internal design

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