Arbitrage Research and Trading

0	Foreword & How to Use the "TG2" Series Most Profitably	i
0.1	Why the TG2 Series of Books?	ii
0.2	What is, and is not, important, and who is this for anyway?	iii
0.2.1	Who is this (book/Series) for?	iv
0.2.2	Pedagogical issues	v
0.2.3	Notation, Grammar, Spelling	vi
0.2.4	About Accompanying (free) software, and Commercial Software.	vii
0.2.5	About these books and relationship to ARTSchool	viii
0.3	Future direction & Road Map for the Series.	ix
0.4	About the Authors	x
0.4.1	Invitation for Contribution	x

1	Introduction to the "TG2… Read Me First" book	1
1.1	Feeds, Screens, and Calculators	2
1.2	What we do for a living	3

PART I: Market Basics

2	Market Basics - Overview	5
2.1	Basics of Finance, Trading, and Business (in the Real World)	5
2.1.1	Business Mandate, and Overview of Strategies & Tools for Profit & Risk	6
2.1.2	Cash is King - "show me the money"	9
2.1.3	Supply/Demand, and Prices	11
2.1.4	The Participants & (Economic) Needs	15
2.1.5	Trading-floor/Trading-operation layout	35
2.1.6	Forecasting vs. Arbitrage & (Forward) Fair Value	41
2.1.7	Spot/Forward Arbitrage Example: 3M-Forward Ferraris	49
2.1.8	Cross-Market Arbitrage Example: Interest Rate Parity	53
2.1.9	Risk and Return	56
2.1.10	The Efficient Frontier and CAPM/APT	65
2.1.11	Holding Period Risk/Return and (Optimal) PaR	69
2.1.12	Reality Impact	76
2.1.13	What Role Does Economics Have in Trading?	78
2.1.14	What Role Does Mathematical Modelling Have in Trading?	81
2.1.15	Market Basics: Overview Summary - The Story so Far	83

3	Market Basics - The Trading Cycle, Trading Discipline, and Management	87
3.1	What/How/Why we trade: Transactions Basics	88
3.1.1	Asset Classes: Equities, IR/FX, and Commodities	88
3.1.2	Description of a few important types of contracts and "payouts"	91
3.1.3	Transaction Basics and (some) Terminology	103
3.2	The Business of Trading	107
3.2.1	The Trading Cycle	108
3.2.2	How and why we trade: The basics of strategies and discipline	115
3.2.3	Examples of where/how money is made in trading/investment banking	130
3.2.4	Funding, Costs, and Capital - this is real money	157
3.2.5	Position Reporting & Accounting	166
3.2.6	Position Reporting vs. Performance Measurement	171
3.2.7	Managing Trading, Traders, and Compensation	178

4	Market Basics - Risk Management & Position Keeping - Part 1	187
4.1	What is Risk & Types of Risk	188
4.1.1	Types of Risk	188
4.1.2	Traditional Measures of (primarily market) Risk	190
4.2	Holding Period vs. Instantaneous Risk Methods, and PaR	202
4.2.1	Holding Period Risk Management - Parameterisation Selection	202
4.2.2	Holding Period Risk Management - Strategy Selection	204
4.2.3	Holding Period Risk Management - Strategy Switching	206
4.3	Position Keeping vs. Risk Management	208
4.3.1	Does the Risk Management Department Exist Purely for "Show"?	208
4.3.2	(Qualitative) Examples of Position Keeping	212
4.4	Proactive Approaches ( … heaven forbid)	213
4.4.1	Heuristic and Informal Proactive Processes	214
4.4.2	Forecast-free Proactive Methods: Surfaces, Scenarios, etc	216
4.4.3	Holding Period Proactive Methods: PaR	221
4.5	Valuation and Risk Reporting	222
4.5.1	Typical Risk Reports	222
4.5.2	Extended Risk Reports, and (other) Complications	225
4.5.3	Operational Issues Trade Booking and Risk Reporting/Management	227
4.5.4	Revisiting P&L, Risk-Adjusted Reporting, and Bonuses	228
4.6	The Management of Risk vs. Risk Management: the Story so Far	229
4.6.1	The Risk Management Big Picture	229
4.6.2	Risk Management Operational Matters	230
4.6.3	Other (Risk) Managerial Matters	231
4.6.4	Management, Risk Management, and Compensation	231

5	Market Basics - A Few Easy but Important (mini) Cases	235
5.1	A Few Notable (mini) Cases	235
5.1.1	Know Your Contract	235
5.1.2	Did you really do the trade?	236
5.1.3	Correlation vs. Efficiency: liquidity in hedging and replication	237
5.1.4	There is no Arb without liquidity - 1: Foreign restricted equity arbitrage.	238
5.1.5	There is no Arb without liquidity - 2: Convertible bond arbitrage	239
5.1.6	There is no Arb without liquidity - 3:  Portfolio Insurance & Oct 1987.	241
5.1.7	There is no Arb without liquidity - 4:  GBP swaptions arbitrage.	242
5.1.8	Front Office vs. Back Office: mark-to-market prices	243
5.1.9	Front Office vs. Back Office: systems & valuation models	244
5.1.10	Barings, Sumitomo, Daiwa, & Kidder Peabody: the "Rogue Trader" Syndrome	246
5.1.11	The "birth" of Credit Derivatives: Risk, Supply Push, and "Hype"	249
5.1.12	KYC:  Bankers Trust vs. Procter & Gamble	252

PART I: Summary	253

PART II: Valuation and Risk Management Basics

6	Valuation and Risk Modelling Basics	259
6.1	Why are mathematical methods required?	259
6.2	Type of maths required - Model vs. Solution	260
6.2.1	Mathematical modelling - rate of return vs. bank balance	260
6.2.2	Mathematical Solutions - Closed form vs. Numerical	262
6.2.3	Numerical methods	262

7	Valuation and Risk Under Certainty	265
7.1	A Short Review of Present Value Theory	266
7.2	Review of usual discounting measures	266
7.2.1	Discount Factors	267
7.2.2	(Spot) Interest Rates	268
7.2.3	Frequency Conversion	271
7.2.4	Forward Rates	272
7.3	IR Curves and discounting multiple cash flows	275
7.3.1	The Internal Rate of Return	276
7.3.2	A few sundry items	279
7.4	IR Curves in Practice	282
7.4.1	Curves: The Zero-coupon and IRR curve	282
7.4.2	Government, LIBOR, Corporate, etc - Curves	283
7.5	Present Value Theory for the Real World	286

8	Valuation and Risk Under Uncertainty - Part 1	289
8.1	Overview of the underlying issues	291
8.1.1	Mathematical modelling of securities prices	291
8.1.2	Some Simplifying Assumptions for Economics and Finance	292
8.2	Modelling the Price/Returns processes - The Basic Idea	294
8.2.1	The "Goal"	294
8.2.2	A First Qualitative Model of Price Dynamics: Trends and Wobbles.	295
8.3	Developing a First Model for Valuation Under Uncertainty	302
8.3.1	Down to earth explanation of the terminology	303
8.3.2	Expectations	304
8.3.3	Re-coupling and De-coupling Drift	312
8.3.4	Expectations and Distributions Summary	312
8.3.5	Making a Bet or Pricing an Option? - 1st (Crude) Valuations under Uncertainty	314
8.3.6	A First Quasi Forecasting Model of Uncertainty	322
8.3.7	Forecasting Prices vs. Forecasting Returns Re-visited	323
8.4	Developing an Extended & Working First Model of Uncertainty	327
8.4.1	A First "Good" Shape of Uncertainty	328
8.4.2	A First Calibration of the Uncertainty	334
8.4.3	A First Model for the Time Evolution of Uncertainty	337
8.4.4	Formalising the First (proper) Model of Uncertainty	342
8.4.5	Calibration of Uncertainty and Annulisation	359
8.5	Putting it all together: A First "Complete" Model for Valuation Under Uncertainty	360
8.5.1	First Valuation of Digital Options	361
8.6	Other Models for Valuation Under Uncertainty	369
8.7	Summary: A First "Complete" Model for Valuation Under Uncertainty	371

9	Risk Management & Position Keeping - Part 2	375
9.1	Introduction to Sensitivity Based Risk Reporting & Hedging	377
9.1.1	Sensitivity Matching and Hedging - The Basic Idea	377
9.1.2	Position Sensitivity Measures	380
9.1.3	Sensitivity of Sensitivity	394
9.1.4	Multi-Dimensional Sensitivities	399
9.1.5	Basic Sensitivity Hedge: Bond/Bond and Bond/Futures	403
9.1.6	Basic Sensitivity Hedge: Options Delta & Delta/Gamma/Rho (Pyramid) Hedging	409
9.1.7	Scenarios of Sensitivities and Risk	423
9.1.8	(Almost) Everything has Term-Structure and Curves	428
9.1.9	Sensitivities and "Greeks" Summary	434
9.2	Introduction to Profile Matching	438
9.2.1	Pension Fund Cash Flow Matching & Immunisation	439
9.2.2	Position keeping with "Singularities" and Model "Mismatch"	444
9.3	Introduction to VaR Based Risk Reporting (and Hedging?)	449
9.3.1	Illustration of the Basic VaR Idea	450
9.3.2	Introduction to Types of VaR Measurement	456
9.3.3	Historical methods: HVaR	458
9.3.4	Covariance VaR Methods: CVaR	465
9.3.5	Monte Carlo methods: MCVaR	471
9.3.6	Backtesting and Verification of VaR	472
9.3.7	Credit VaR based methods	473
9.3.8	Reality Impact and Future Considerations	474
9.3.9	Basic VaR Summary	478

10	Trading with Arbitrage-Free/Risk Neutral Methods - Part 1	481
10.1	Risk Neutral Valuation - The Coffee Table Edition	483
10.1.1	The Risk Neutral Valuation - The (easy) Math Edition	485
10.1.2	Risk Neutral vs. Risk Preference Forecasting Models	495
10.1.3	An Application of Risk Neutral Valuation: Black-Scholes Options Pricing	497
10.2	Trading with Risk-Neutral Valuation Under Uncertainty	505
10.2.1	Synthetic Replication Delta Hedging Example 1	506
10.2.2	Synthetic Replication Delta Hedging Example 2	515
10.2.3	Synthetic Replication Gamma Hedging Example	518
10.2.4	Provisioning - The Opposite of Dynamic Replication	522
10.3	Risk Neutral Valuation Summary	524

11	Volatility Basics	527
11.1	Statistical (or Empirical, or Historical) Volatility	528
11.1.1	Characterising (empirical) Volatility	528
11.1.2	Sampling length, Frequency, and Calendar Effects	532
11.1.3	Correlation/Covariance	539
11.1.4	Price vs. Returns (and Absolute vs. Relative)	541
11.1.5	Histories of "Historicals"	544
11.1.6	Relationship to Distributions and Calibration	547
11.2	Model (and Implied) Volatility	548
11.2.1	Implied Volatility(s)	549
11.2.2	Implied vs. Historical (Model) Volatility	551
11.2.3	Exotic and Structured (Model) Volatility	554
11.2.4	Term-Structure Model Volatility	561
11.3	Representations of Quoted/Traded Volatility	564
11.3.1	Term structure of (Market & Model) Volatility as Curves & Surfaces	565
11.3.2	Volatility Skew	572
11.3.3	Mean Reverting Volatility and Other Effects	575
11.3.4	HJM: volatility isn't everything, it's the only thing	577
11.4	"Trading" Volatility	578
11.5	"P&L" Volatility	581
11.6	Advanced Volatility Concepts	583
11.7	Volatility Basics Summary	591

12	PaR: P&L Based Valuation, Risk Management, and Validation	595
12.1	Introduction to the PaR Methodology	599
12.1.1	Trading, Hedging, Selling, Managing, and Real World P&L	599
12.1.2	Trading, Hedging, Selling, Managing, and Simulated P&L	600
12.2	Comments on Software and Programming Issues	602
12.3	Forward Testing vs. Back Testing	604
12.3.1	Generating Forward Market Scenarios	605
12.3.2	Back Testing with Historical Market Data	607
12.4	Embedding a Dealing System in a Scenario Generator	610
12.5	Embedding Strategies:  Prop Trading & Position Keeping Rules	612
12.6	Accounting & Reporting: Cash Flow vs. P&L, Inter-period Risk(s), and Much More	614
12.7	Risk-adjusted Performance Calculations	616
12.8	"Optimal" Holding Period Risk-Adjusted Returns PaR via Efficient Frontiers	617
12.9	What a PaR Calculator Might "Look Like"	619
12.9.1	A Spreadsheet Example (Suitable for simple positions)	619
12.9.2	A "full blown" Example (Suitable for almost anything)	622
12.10	Mathematically Optimal vs. Holding Period P&L Optimal Trading & Hedging	627
12.11	A Simple Forward/Backward PaR Example: Bonds/Bond Futures	629
12.11.1	Forward Testing (with a 1-factor Model)	629
12.11.2	Back Testing the Hedging Strategy and the (1-factor) model	632
12.12	PaR Summary: Theory vs. Reality	635

PART II: Summary	637

Appendices	1
Appendix A: Notation/Abbreviations	2
Abbreviations	2
Currencies	4
Greek Letters	5
Alphanumeric Letters	5
Mathematical Operators	5
Appendix B: ARTicles	1
B1: ARTicles: An Efficient Frontier Primer	1
B2: ARTicles: Optimisation and P&L - Part 1	1
B3: ARTicles: How much to pay a trader?	1
B4: ARTicles: Chaos and Predictability in Finance - Part 1: Are Markets Random?	1
B5: ARTicles: Chaos and Predictability in Finance - Part 2: Periodicity and Aperiodicity	1
B6: ARTicles: Chaos and Predictability in Finance - Part 3: Fractals and Options Trading	1
B7: ARTicles: Term-Structure Calibration: Nonsense & Reality	1
B8: ARTicles: A Principal Components and Term Structure Models Quickie	1
References	i
Subject Index	i