Derivatives and internal models: modern risk management
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English German |
| Published: |
Basingstoke [u.a.]
Macmillan
1999
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXI, 371 S. graph. Darst. |
| ISBN: | 0333750691 |
Staff View
MARC
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Contents
List of Figures, Tables and Examples viii
Foreword by Wolfgang M. Schmidt xiii
Preface xv
Acknowledgements xviii
List of Abbreviations and Symbols xix
1 Introduction 1
2 Legal Background 5
3 The Basic Risks of the Market 9
3.1 Interest rates 9
3.2 Market prices 16
3.3 A model for the basic risks of the market 16
4 Financial Instruments: A Classification of Derivatives and
Underlyings 27
4.1 Spot trading 28
4.2 Derivative securities 36
4.3 Options 39
5 Valuation Methods for Financial Instruments 42
5.1 Review of the prerequisites 42
5.2 Present values, yields and traditional risk measures 44
5.3 Arbitrage 59
5.4 Binomial methods: Cox, Ross and Rubinstein 66
5.5 Martingales and risk neutrality 73
v
Contents
5.6 Exact analytical methods: Black Scholes 77
5.7 Black 76 for interest rate derivatives 83
5.8 Monte Carlo simulations 86
6 Hedging 100
6.1 Prerequisites 100
6.2 Synthetic derivatives and the Black Scholes differential
equations 100
6.3 'Greek' risk management using sensitivities 109
7 Pricing and Hedging the Most Important Instruments 118
7.1 Spot transactions on interest rates 118
7.2 Forward rate agreements and interest rate futures 143
7.3 Plain vanilla options and futures 156
7.4 Index options and futures 161
7.5 Currency options and futures 162
7.6 Interest rate options 164
7.7 Exotic options 176
7.8 Structured instruments and stripping 195
8 Risk Management 218
8.1 From the volatility of a risk factor to the volatility of
a portfolio 219
8.2 Value at risk, confidence level and liquidation period 221
8.3 The covariance matrix 226
8.4 Cash flow structures and interest rate risks 227
8.5 Interpolations and cash flow mapping 240
8.6 The variance covariance method 244
8.7 Monte Carlo simulation 252
8.8 Historical simulation 255
8.9 Crash and stress testing: worst case scenarios 258
vi
Contents
8.10 The pros and cons of the common value at risk
methods 259
8.11 Backtesting: a check of the applied method 260
8.12 Organizational implementation of risk
management 266
9 The Determination of Market Parameters 280
9.1 Arbitrage free term structures of interest rates 280
9.2 Implied volatilities, smiles and volatility indices 293
9.3 Yields, volatility and correlation from historical rate
movements 295
9.4 Conversion from yield to price volatility 297
9.5 Conversion of volatilities and correlations into another
currency 298
9.6 Estimation of errors 305
10 Probability Theory and Statistics 313
10.1 Probability, expectation value and variance 313
10.2 Multivariate distributions, covariance, correlation and beta 314
10.3 Some important distributions 317
10.4 Transformations from one kind of distribution to another 322
10.5 Stochastic processes and Ito's Lemma 324
Glossary 326
Notes 349
Bibliography 357
Index 363
vii
List of Figures, Tables and
Examples
FIGURES
3.1 The general discount factor for the time period from t to T 10
3.2 The sequence of times t, Tand T 12
3.3 The general discount factor for the forward rate agreed upon
at time t for the period from T to V 13
3.4 A random walk consisting of 8 steps in 2 dimensions 17
3.5 The closing price of a stock over a period of 500 trading days 20
3.6 The distributions of Table 3.2 with ndt = 0 and a \fdt = 1 25
4.1 Common money market securities 29
4.2 Common capital market securities 34
5.1 A recombining tree 70
5.2 The circle with 2m diameter within the square with 2m
side length 88
5.3 Simulation of In [S(t)/S(0)] with standardized normal distributed
random numbers 94
5.4 The same random walk as Figure 5.3 with yield 6% p.a. 94
7.1 The prices of bonds taken from Example 4 123
7.2 Reduction of the interest rate risk of a bond via a plain vanilla
interest rate swap 128
7.3 The range of possible lines connecting two points with
identical measurement errors, which lie either far apart or
close to each other 189
7.4 Conversion of a structured bond by means of an asset swap 202
8.1 The limits between the 3 zones and the add on for the
maximum number of outliers permitted as functions of n 265
10.1 2000 uniformly distributed and transformed random
numbers 323
TABLES
3.1 Factors for interest calculation for the 4 most important
compounding methods 11
viii
List of Figures, Tables and Examples
3.2 Statistical properties of the logarithm of a risk factor and the
risk factor itself 24
4.1 Public sector securities 31
4.2 Example of international money market instruments 33
4.3 Interest payment conventions in important bond markets 36
5.1 An overview of the different interest rates 51
5.2 Two portfolios exemplifying the use of arbitrage arguments for
the derivation of prices 60
5.3 Lower and upper bounds for the value of plain vanilla options 63
5.4 Two portfolios exemplifying put call parity by means of
arbitrage considerations 65
5.5 Put call parities for plain vanilla options 66
5.6 Significance of the terms appearing in Black Scholes
equations 80
5.7 The 'recipe' for Monte Carlo simulation 92
6.1 Sensitivities of derivatives and the underlying itself with respect
to the spot price S(t) 108
6.2 Definition of 'Greek risk measures' 110
7.1 Present value and sensitivities of a zero bond for the
4 compounding methods 119
7.2 Long short conventions for swaps and swaptions 128
7.3 Categorization and 'brute force' valuation methods for
exotic options 180
7.4 The parameter values to be inserted in (7.64) for the valuation
of all 'knock out' options 185
7.5 Stripped bonds and their issuers 197
7.6 The most common day count conventions 207
7.7 Adjustment conventions 208
8.1 The pros and cons of the common value at risk methods 259
8.2 The backtesting criteria and multipliers used for the review
of internal models 265
8.3 Interest rate term structures for different credit qualities 269
8.4 Summary of the most significant market risks of common
products 270
8.5 Common financial instruments and their linear sensitivities 272
EXAMPLES
1 Forward rates starting in 1 15 years for maturity periods between
1 and 15 years 15
2 The cash flow spreadsheet of a portfolio 49
3 Prices and risk measures for a sample call option using (5.43) 112
ix
List of Figures, Tables and Examples
4 Valuing of bonds using spot rates and par rates assuming annual
coupon payments and discrete compounding 124
5 The sensitivities of the coupon bonds from Example 4 127
6 The cash flow table of a swap 130
7 The coupon bond replicating the cash flow structure of an
annuity loan with semi annualized discrete compounding 136
8 The cash flow table of the annuity loan in Example 7 139
9 Forward swap fixed with a 12 month floating reference rate in
3 years for 10 years 152
10 The forward par swap corresponding to Example 9 153
11 The input parameters of the options and futures examples 156
12 Calculation of plain vanilla spot and future options using the
Black Scholes model 158
13 Valuation of European plain vanilla options using the binomial
distribution with n = 100 time steps 159
14 Calculation of the futures price 5' of an American option C on
the spot price S, and of an American option C on the futures price 160
15 Caplets and floorlets as options on zero bonds 169
16 Interest rate options with a 12 month floating reference rate 172
17 Valuation of swaptions 175
18 Swaptions as options on coupon bonds 175
19 Basic features of a Bundesanleihe: 1 197
20 Cash flows of a Bundesanleihe 197
21 Basic features of a coupon strip 198
22 Cash flows of a coupon strip 199
23 Basic features of a LIBOR strip 199
24 Cash flows of a LIBOR strip 200
25 Basic features of a step up callable bond 202
26 Cash flows of the step up bond in case the bond is not called 203
27 Example of the basic features of a step up callable bond 204
28 Basic features, valuation and risk measures of a step up
callable bond 206
29 Time calculation using different day count conventions 208
30 Business day convention: 1 209
31 Business day convention: 2 210
32 Business day convention: 3 211
33 Business day convention: 4 211
34 Basic features of a Bundesanleihe: 2 213
35 Adjustment of payment date 214
36 Adjustment for bonds without a 'fix' convention 215
37 Maturity date as basis of rollover day 216
38 Explicit arrangement of rollover day 216
39 The value at risk of a portfolio 249
40 Sensitivities of a sample portfolio of interest rate instruments 274
x
List of Figures, Tables and Examples
41 Price of an interest rate instrument depending on the yield
scenario 276
42 Calculation of the spot rate for maturity up to 30.06.2002
using the closed form solution and the bootstrap
method 284
43 Day count and business day conventions used in discount
factors examples 287
44 Money market rates 287
45 Swap rates 287
46 Discount factors from the money market rates 288
47 Discount factors, 2 4 years 290
48 Discount factors, 5 7 years 290
49 Discount factors, 8 10 years 291
50 Fully stripped par yield curve resulting in the spot rate curve 292
51 The method of exponential interpolation 293
52 The risk factors of the example portfolio 300
53 Conversion of exchange rate and risk factor volatilities and
correlations from the original 'domestic' currencies to
DEM and USD 304
54 Estimation of yield, volatility and their errors from semi annual
relative price changes x 310
xi |
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| indexdate | 2025-03-20T19:10:42Z |
| institution | BVB |
| isbn | 0333750691 |
| language | English German |
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| spelling | Deutsch, Hans-Peter Verfasser (DE-588)115872647 aut Derivatives and internal models modern risk management Hans-Peter Deutsch and Roland Eller Basingstoke [u.a.] Macmillan 1999 XXI, 371 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hedging gtt Risk management gtt Termijnhandel gtt Derivative securities Risk management Derivat Wertpapier (DE-588)4381572-8 gnd rswk-swf Bewertung (DE-588)4006340-9 gnd rswk-swf CD-ROM (DE-588)4139307-7 gnd rswk-swf Risikomanagement (DE-588)4121590-4 gnd rswk-swf Hedging (DE-588)4123357-8 gnd rswk-swf Finanzinstrument (DE-588)4461672-7 gnd rswk-swf Finanzinstrument (DE-588)4461672-7 s Hedging (DE-588)4123357-8 s Risikomanagement (DE-588)4121590-4 s CD-ROM (DE-588)4139307-7 s 1\p DE-604 Derivat Wertpapier (DE-588)4381572-8 s Bewertung (DE-588)4006340-9 s 2\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009006917&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Deutsch, Hans-Peter Derivatives and internal models modern risk management Hedging gtt Risk management gtt Termijnhandel gtt Derivative securities Risk management Derivat Wertpapier (DE-588)4381572-8 gnd Bewertung (DE-588)4006340-9 gnd CD-ROM (DE-588)4139307-7 gnd Risikomanagement (DE-588)4121590-4 gnd Hedging (DE-588)4123357-8 gnd Finanzinstrument (DE-588)4461672-7 gnd |
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| title | Derivatives and internal models modern risk management |
| title_auth | Derivatives and internal models modern risk management |
| title_exact_search | Derivatives and internal models modern risk management |
| title_full | Derivatives and internal models modern risk management Hans-Peter Deutsch and Roland Eller |
| title_fullStr | Derivatives and internal models modern risk management Hans-Peter Deutsch and Roland Eller |
| title_full_unstemmed | Derivatives and internal models modern risk management Hans-Peter Deutsch and Roland Eller |
| title_short | Derivatives and internal models |
| title_sort | derivatives and internal models modern risk management |
| title_sub | modern risk management |
| topic | Hedging gtt Risk management gtt Termijnhandel gtt Derivative securities Risk management Derivat Wertpapier (DE-588)4381572-8 gnd Bewertung (DE-588)4006340-9 gnd CD-ROM (DE-588)4139307-7 gnd Risikomanagement (DE-588)4121590-4 gnd Hedging (DE-588)4123357-8 gnd Finanzinstrument (DE-588)4461672-7 gnd |
| topic_facet | Hedging Risk management Termijnhandel Derivative securities Derivat Wertpapier Bewertung CD-ROM Risikomanagement Finanzinstrument |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009006917&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT deutschhanspeter derivativesandinternalmodelsmodernriskmanagement |