An Arbitrage Guide to Financial Markets

1 The Purpose and Structure of Financial Markets 1

1.1 Overview 1

1.2 Risk sharing 2

1.3 The structure of financial markets 8

1.4 Arbitrage: Pure vs. relative value 12

1.5 Financial institutions: Asset transformers and broker-dealers 16

1.6 Primary and secondary markets 18

1.7 Market players: Hedgers vs. speculators 20

1.8 Preview of the book 22

Part One SPOT 25

2 Financial Math I—Spot 27

2.1 Interest-rate basics 28

Present value 28

Compounding 29

Day-count conventions 30

Rates vs. yields 31

2.2 Zero, coupon and amortizing rates 32

Zero-coupon rates 32

Coupon rates 33

Yield to maturity 35

Amortizing rates 38

Floating-rate bonds 39

2.3 The term structure of interest rates 40

Discounting coupon cash flows with zero rates 42

Constructing the zero curve by bootstrapping 44

2.4 Interest-rate risk 49

Duration 51

Portfolio duration 56

Convexity 57

Other risk measures 58

2.5 Equity markets math 58

A dividend discount model 60

Beware of P/E ratios 63

2.6 Currency markets 64

3 Fixed Income Securities 67

3.1 Money markets 67

U.S. Treasury bills 68

Federal agency discount notes 69

Short-term munis 69

Fed Funds (U.S.) and bank overnight refinancing (Europe) 70

Repos (RPs) 71

Eurodollars and Eurocurrencies 72

Negotiable CDs 74

Bankers’ acceptances (BAs) 74

Commercial paper (CP) 74

3.2 Capital markets: Bonds 79

U.S. government and agency bonds 83

Government bonds in Europe and Asia 86

Corporates 87

Munis 88

3.3 Interest-rate swaps 90

3.4 Mortgage securities 94

3.5 Asset-backed securities 96

4 Equities, Currencies, and Commodities 101

4.1 Equity markets 101

Secondary markets for individual equities in the U.S. 102

Secondary markets for individual equities in Europe and Asia 103

Depositary receipts and cross-listing 104

Stock market trading mechanics 105

Stock indexes 106

Exchange-traded funds (ETFs) 107

Custom baskets 107

The role of secondary equity markets in the economy 108

4.2 Currency markets 109

4.3 Commodity markets 111

5 Spot Relative Value Trades 113

5.1 Fixed-income strategies 113

Zero-coupon stripping and coupon replication 113

Duration-matched trades 116

Example: Bullet–barbell 116

Example: Twos vs. tens 117

Negative convexity in mortgages 118

Spread strategies in corporate bonds 121

Example: Corporate spread widening/narrowing trade 121

Example: Corporate yield curve trades 123

Example: Relative spread trade for high and low grades 124

5.2 Equity portfolio strategies 125

Example: A non-diversified portfolio and benchmarking 126

Example: Sector plays 128

5.3 Spot currency arbitrage 129

5.4 Commodity basis trades 131

Part Two FORWARDS 133

6 Financial Math II—Futures and Forwards 135

6.1 Commodity futures mechanics 138

6.2 Interest-rate futures and forwards 141

Overview 141

Eurocurrency deposits 142

Eurodollar futures 142

Certainty equivalence of EDfutures 146

Forward-rate agreements (FRAs) 147

Certainty equivalence of FRAs 149

6.3 Stock index futures 149

Locking in a forward price of the index 150

Fair value of futures 150

Fair value with dividends 152

Single stock futures 153

6.4 Currency forwards and futures 154

Fair value of currency forwards 155

Covered interest-rate parity 156

Currency futures 158

6.5 Convenience assets—backwardation and contango 159

6.6 Commodity futures 161

6.7 Spot–Forward arbitrage in interest rates 162

Synthetic LIBOR forwards 163

Synthetic zeros 164

Floating-rate bonds 165

Synthetic equivalence guaranteed by arbitrage 166

6.8 Constructing the zero curve from forwards 167

6.9 Recovering forwards from the yield curve 170

The valuation of a floating-rate bond 171

Including repo rates in computing forwards 171

6.10 Energy forwards and futures 173

7 Spot–Forward Arbitrage 175

7.1 Currency arbitrage 176

7.2 Stock index arbitrage and program trading 182

7.3 Bond futures arbitrage 187

7.4 Spot–Forward arbitrage in fixed-income markets 189

Zero–Forward trades 189

Coupon–Forward trades 191

7.5 Dynamic hedging with a Euro strip 193

7.6 Dynamic duration hedge 197

8 Swap Markets 199

8.1 Swap-driven finance 199

Fixed-for-fixed currency swap 200

Fixed-for-floating interest-rate swap 203

Off-market swaps 205

8.2 The anatomy of swaps as packages of forwards 207

Fixed-for-fixed currency swap 208

Fixed-for-floating interest-rate swap 209

Other swaps 210

Swap book running 210

8.3 The pricing and hedging of swaps 211

8.4 Swap spread risk 217

8.5 Structured finance 218

Inverse floater 219

Leveraged inverse floater 220

Capped floater 221

Callable 221

Range 222

Index principal swap 222

8.6 Equity swaps 223

8.7 Commodity and other swaps 224

8.8 Swap market statistics 225

Part Three OPTIONS 231

9 Financial Math III—Options 233

9.1 Call and put payoffs at expiry 235

9.2 Composite payoffs at expiry 236

Straddles and strangles 236

Spreads and combinations 237

Binary options 240

9.3 Option values prior to expiry 240

9.4 Options, forwards and risk-sharing 241

9.5 Currency options 242

9.6 Options on non-price variables 243

9.7 Binomial options pricing 244

One-step examples 244

A multi-step example 251

Black–Scholes 256

Dividends 257

9.8 Residual risk of options: Volatility 258

Implied volatility 260

Volatility smiles and skews 261

9.9 Interest-rate options, caps, and floors 264

Options on bond prices 265

Caps and floors 265

Relationship to FRAs and swaps 267

An application 268

9.10 Swaptions 269

Options to cancel 270

Relationship to forward swaps 270

9.11 Exotic options 272

Periodic caps 272

Constant maturity options (CMT or CMS) 273

Digitals and ranges 273

Quantos 274

10 Option Arbitrage 275

10.1 Cash-and-carry static arbitrage 275

Borrowing against the box 275

Index arbitrage with options 277

Warrant arbitrage 278

10.2 Running an option book: Volatility arbitrage 279

Hedging with options on the same underlying 279

Volatility skew 282

Options with different maturities 284

10.3 Portfolios of options on different underlyings 284

Index volatility vs. individual stocks 285

Interest-rate caps and floors 286

Caps and swaptions 287

Explicit correlation bets 288

10.4 Options spanning asset classes 289

Convertible bonds 289

Quantos and dual-currency bonds with fixed conversion rates 290

Dual-currency callable bonds 291

10.5 Option-adjusted spread (OAS) 291

10.6 Insurance 292

Long-dated commodity options 293

Options on energy prices 294

Options on economic variables 294

A final word 294

Appendix CREDIT RISK 295

11 Default Risk (Financial Math IV) and Credit Derivatives 297

11.1 A constant default probability model 298

11.2 A credit migration model 300

11.3 Alternative models 301

11.4 Credit exposure calculations for derivatives 302

11.5 Credit derivatives 305

Basics 306

Credit default swap 306

Total-rate-of-return swap 307

Credit-linked note 308

Credit spread options 308

11.6 Implicit credit arbitrage plays 310

Credit arbitrage with swaps 310

Callable bonds 310

11.7 Corporate bond trading 310

Index 313