An Introduction to Value-at-Risk

Foreword xv
 
Preface xvii
 
Preface to the first edition xxi
 
About the author xxiii
 
1 INTRODUCTION TO RISK 1
 
Defining risk 2
 
The elements of risk: characterising risk 3
 
Forms of market risk 4
 
Other risks 5
 
Risk estimation 6
 
Risk management 7
 
The risk management function 7
 
Managing risk 9
 
Quantitative measurement of risk-reward 9
 
Standard deviation 10
 
Sharpe Ratio 10
 
Van Ratio 11
 
2 VOLATILITY AND CORRELATION 13
 
Statistical concepts 14
 
Arithmetic mean 14
 
Probability distributions 16
 
Confidence intervals 18
 
Volatility 20
 
The normal distribution and VaR 26
 
Correlation 28
 
3 VALUE-AT-RISK 29
 
What is VaR? 30
 
Definition 30
 
Methodology 32
 
Centralised database 32
 
Correlation assumptions 33
 
Correlation method 33
 
Historical simulation method 34
 
Monte Carlo simulation method 35
 
Validity of the volatility-correlation VaR estimate 35
 
How to calculate VaR 35
 
Historical method 36
 
Simulation method 37
 
Variance-covariance, analytic or parametric method 37
 
Mapping 44
 
Confidence intervals 47
 
Comparison between methods 48
 
Choosing between methods 48
 
Comparison with the historical approach 53
 
Comparing VaR calculation for different methodologies 54
 
Summary 56
 
4 VALUE-AT-RISK FOR FIXED INTEREST INSTRUMENTS 59
 
Fixed income products 60
 
Bond valuation 60
 
Duration 62
 
Modified duration 64
 
Convexity 64
 
Interest rate products 65
 
Forward rate agreements 65
 
Fixed income portfolio 68
 
Applying VaR for a FRA 70
 
VaR for an interest rate swap 72
 
Applying VaR for a bond futures contract

Moorad Choudhry is an MD in Group Treasury at The Royal Bank of Scotland. He is Visiting Professor at the Department of Mathematical Sciences, Brunel University, Visiting Professor at the IFS-School of Finance, Visiting Teaching Fellow at the Department of Management, Birkbeck, University of London, Vice-Chair of the Board of Directors of PRMIA, and Fellow of the Chartered Institute for Securities & Investment.