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Pricing and Hedging Financial Derivatives: A Guide for Practitioners

توضیحات

Pricing and Hedging Financial Derivatives: A Guide for Practitioners attempts to explain the insights required in the pricing and hedging of the most common derivative products and aims to educate and inform the many rather than the few. Targeted at the practitioner rather than the academic, this book contains many worked examples to help develop an understanding of key concepts and tools.

The book begins with a descriptive examination of the main asset classes, the main derivative products and the most common option strategies. It then moves on to the fundamentals of option pricing, the Greeks, implied volatility, the volatility smile, exotic derivatives (digitals, barriers, Asian options) and multi-asset derivatives. Along the way, the authors spend time explaining the concepts of replication and risk-neutral valuation with numerous examples that help develop an intuitive grasp of derivative pricing. The book concludes with a chapter on structured products because these, unlike derivative products, may be accessible to investors.

A website accompanies the book (www.wiley.com/go/financialderivatives) and contains a number of practical example excel spreadsheets.

The book will provide investment professionals, whether new to the world of finance or seasoned, with the toolkit required to understand derivatives and approach them with confidence.


LEONARDO MARRONI is an asset manager with the Emerging Markets team at GLG Partners in London. He joined in January 2010 from Barclays where he was working as a structurer in the commodities division. Before joining Barclays, Leonardo worked in the equity structured products trading team at Banca Caboto in London where he was responsible for structuring and trading algorithmic products. Prior to this, Leonardo was part of the interest rates derivatives trading team at Banca Caboto in Milan. Leonardo graduated in Economics from Bocconi University in Milan.

IRENE PERDOMO trades base metals at Noble in Singapore. Prior to this, she worked as a structurer for the commodities division of Barclays in London. Irene has an MBA from IESE Business School in Barcelona. She is a native of Uruguay and she studied Computer Science Engineering in Montevideo. She also spent time studying finance at the University of Chicago Booth School of Business. Before working in the finance industry, she worked in IT, in South America and the Indian sub-continent.

Preface ix

Acknowledgements xi

1 An Introduction to the Major Asset Classes 1

1.1 Equities 1

1.1.1 Introduction 1

1.1.2 Pricing equities 2

1.1.3 Fundamental analysis 2

1.1.4 Technical analysis 3

1.1.5 Quantitative analysis 3

1.1.6 The equity risk premium and the pre-FOMC announcement drift 5

1.2 Commodities 5

1.2.1 Introduction 5

1.2.2 Hedging 6

1.2.3 Backwardation and contango 7

1.2.4 Investment in commodities 9

1.2.5 Commodity fundamentals 10

1.2.6 Super-cycles in commodity prices 11

1.2.7 Future regulation 12

1.3 Fixed Income 12

1.3.1 Introduction 12

1.3.2 Credit risk 13

1.3.3 The empirical pattern of yield curve moves 13

1.3.4 Modelling interest rate movements 14

1.3.5 Modelling the risks of default 14

1.4 Foreign Exchange 15

1.4.1 Introduction 15

1.4.2 How foreign exchange rates are quoted 16

Summary 17

2 Derivatives: Forwards, Futures and Swaps 19

2.1 Derivatives 19

2.2 Forward Contracts 20

2.2.1 Definition 20

2.2.2 Payoffs of forward contracts 21

2.2.3 Forward price versus delivery price 23

2.3 Futures Contracts 24

2.4 Calculating Implied Forward Prices and Valuing Existing Forward Contracts 26

2.4.1 Calculating implied forward prices on equities 26

2.4.2 Calculating implied forward prices on foreign exchange rates 29

2.4.3 Calculating implied forward prices on commodities 31

2.4.4 Valuing existing forward contracts 34

2.5 Pricing Futures Contracts 34

2.6 Swaps 35

2.6.1 Introduction 35

2.6.2 Interest rate swaps 36

2.6.3 Commodity swaps 41

2.6.4 Commodity swap valuation 44

2.6.5 Commodity swaps with variable notional and price 46

2.6.6 Currency swaps 46

2.6.7 Equity swaps 48

Summary 49

3 Derivatives: Options and Related Strategies 51

3.1 Call Options 51

3.1.1 Definition 51

3.1.2 Examples 52

3.1.3 Scenario analysis for the S&P 500 Index call option 53

3.2 Put Options 55

3.2.1 Definition 55

3.2.2 Examples 55

3.2.3 Scenario analysis for put options 56

3.3 Boundary Conditions for Call and Put Options Prices 58

3.3.1 Introduction and basic notation 58

3.3.2 A call option cannot be worth more than the price of the underlying asset 59

3.3.3 The price of a put option cannot be higher than the present value of the strike price, K 60

3.3.4 Lower boundaries for call options on non-dividend paying stocks 60

3.3.5 Lower boundaries for put options on non-dividend paying stocks 61

3.4 Put-Call Parity 61

3.5 Swaptions 63

3.6 Options Strategies 64

3.6.1 Introduction to option strategies 64

3.6.2 Option spreads 65

3.6.3 Directional strategies using vertical spreads 65

3.6.4 Risk reversal and collars 69

3.6.5 Volatility strategies with puts and calls 70

Summary 76

4 Binomial Option Pricing 77

4.1 One-Period Binomial Tree: Replication Approach 77

4.2 Risk-Neutral Valuation 83

4.2.1 Introduction to risk-neutral valuation 83

4.2.2 An alternative way to think of the option price 84

4.2.3 Risk-neutral probabilities 85

4.3 Two-Period Binomial Tree: Valuing Back Down the Tree 85

4.4 The Binomial Tree: A Generalization 89

4.5 Early Exercise and American Options 90

4.6 Volatility Calibration 90

Summary 92

5 The Fundamentals of Option Pricing 93

5.1 Intrinsic Value and Time Value of an Option 93

5.1.1 Introduction and definitions 93

5.1.2 Jensen’s inequality 94

5.1.3 Time value of an option 95

5.2 What is Volatility and Why Does it Matter? 95

5.3 Measurement of Realized Volatility and Correlation 97

5.4 Option Pricing in the Black-Scholes Framework 99

5.5 The Option Delta and the Replication of the Option Payoff 100

5.6 Option Replication 102

5.7 Option Replication, Risk-Neutral Valuation and Delta Hedging Revisited 104

5.8 Options on Dividend Paying Assets 106

5.9 Options on Futures: The Black Model 107

5.10 Monte Carlo Pricing 108

5.10.1 Introduction to the Monte Carlo technique 108

5.10.2 Generation of a Monte Carlo path 110

5.11 Other Pricing Techniques 112

5.11.1 Partial differential equation 112

5.11.2 Binomial/trinomial tree pricing 113

5.12 Pricing Techniques Summary 113

5.13 The Excel Spreadsheet “Option Replication” 114

5.13.1 Introduction and description of the spreadsheet 114

5.13.2 Why the replication is not perfect 117

Summary 117

6 Implied Volatility and the Greeks 121

6.1 Implied Volatility 121

6.2 The Greeks 123

6.3 Delta and its Dynamics 123

6.3.1 Definition and calculation 123

6.3.2 The dynamics of delta 125

6.4 Gamma and its Dynamics 127

6.5 Vega and its Dynamics 132

6.6 Theta and its Dynamics 136

6.6.1 Definition and calculation 136

6.6.2 Gamma versus theta: An equilibrium at the heart of option pricing 138

6.6.3 Dynamics of theta 140

6.7 Rho 142

6.8 Option Trading 143

6.8.1 Taking a position on implied volatility or on implied versus realized volatility 143

6.8.2 Taking a position on the terminal payoff or re-hedging with a certain frequency 144

6.9 Some Additional Remarks (in Q&A Format) 146

6.10 An Example of the Behaviour of Implied Volatility: EUR/USD Rate and S&P 500 in 2010-2012 147

Summary 148

7 Volatility Smile and the Greeks of Option Strategies 151

7.1 The Volatility Smile - Why is the Implied Volatility Not Flat Across Different Strikes? 151

7.2 The “Sticky Delta” and “Sticky Strike” Approaches to Describing Volatility Smile 153

7.3 The Volatility Term Structure - Why is the Implied Volatility Not Flat Across Different Expiries? 155

7.4 The Volatility Surface - Combining Smile and Term Structure 156

7.5 Analysing the Greeks of Common Option Strategies 158

7.5.1 Vertical call or put spreads 158

7.5.2 Straddles and strangles 162

7.5.3 Risk reversals 163

7.5.4 Butterflies 165

7.5.5 Butterflies and volatility convexity 168

7.6 Some Additional Remarks on Straddles, Risk Reversals and Butterflies 170

7.7 Vega Hedging is Not Just Simply Offsetting Overall Vega Exposure 171

7.8 Hedging Volatility Risk: A Brief Introduction of the Vanna-Volga Approach 172

7.9 The Volatility Smile - One Step Further 173

7.9.1 Introduction 173

7.9.2 Why and how to build a smile 173

7.9.3 Smile arbitrage 175

7.9.4 Volatility surface 176

7.9.5 Volatility time dependence in forward-based assets 176

7.9.6 Models of forward-based asset volatilities 178

7.9.7 Calibrating a model of forward-based asset volatilities 178

7.10 Pricing Exotic Options 178

7.11 Different Types of Volatility 179

7.11.1 Volatilities discussed so far 179

7.11.2 Forward-starting volatility 179

7.11.3 Local volatility 181

7.11.4 The limits of local volatility 181

7.11.5 Stochastic volatility models 182

7.11.6 Local-stochastic volatility models 183

Summary 184

8 Exotic Derivatives 185

8.1 Exotic Derivatives with Fixed Payoffs 185

8.1.1 European digital options 185

8.1.2 One touch and no touch options 185

8.1.3 Combinations of fixed payoff options 187

8.2 Other Common Exotic Derivatives 188

8.2.1 Barrier options 188

8.2.2 Asian options 190

8.3 European Digital Options: Pricing and Greeks 191

8.3.1 Pricing European digital options 191

8.3.2 The Greeks of a digital option 194

8.3.3 Incorporating volatility skew into the price of a digital option 196

8.4 Other Exotic Options: Pricing and Greeks 200

8.4.1 Pricing common barrier options 200

8.4.2 Greeks of common barrier options 202

8.4.3 Greeks of Asian options 208

Summary 208

9 Multi-Asset Derivatives 209

9.1 Basket Options 209

9.1.1 Basket option definition and Greeks 209

9.1.2 Cross-gamma and correlation revisited 210

9.2 Best-of and Worst-of Options 211

9.2.1 Best-of and worst-of definitions 211

9.2.2 The price and the Greeks of best-of and worst-of options 214

9.2.3 Best-of call 214

9.2.4 Best-of put 215

9.2.5 Worst-of call 218

9.2.6 Worst-of put 219

9.2.7 Cross-gamma and correlation revisited (again. . . ) 221

9.3 Quanto Derivatives 222

9.4 “Compo” Derivatives 225

Summary 227

10 Structured Products 229

10.1 Definition 229

10.2 Common Features 229

10.3 Principal Protection 230

10.4 The Benefit to the Issuer 231

10.5 Redemption Amounts and Participation 232

10.6 Principal at Risk: Embedding a Short Option 234

10.7 More Complicated Payoffs 235

10.7.1 “Shark fin” notes 235

10.7.2 Reverse convertible notes 236

10.7.3 Range accrual notes 236

10.7.4 Auto-callable notes 237

10.8 Auto-Callable Note: Pricing and Risk Profile 238

10.8.1 Pricing 238

10.8.2 Risk profile 239

10.9 One Step Forward: The Worst-of Digital Note 240

10.10 A Real-Life Example of Structured Product 241

10.11 Liquidity and Exchange-Traded Notes (ETNs) 242

Summary 243

Index 245