DERIVATIVES AND RISK MANAGEMENT

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1 A IS 1! foi- 331 DERIVATIVES AND RISK MANAGEMENT RAJIV SRIVASTAVA Professor Indian Institute of Foreign Trade New Delhi QXJFORD UNIVERSITY PRKSS

2 CONTENTS Foreword Preface 1. Derivatives An Introduction Introduction Risk Management 1 Managing Risk 2 -, Types of Business Risks 3 Derivatives 4 Derivative Products 6 Classification of Derivatives 6 Participants in Derivative Markets 9 Evolution of Derivatives 11 Functions of Derivative Markets 16 Misuses, Criticism of Derivatives Forwards and Futures Introduction 22 Forward Contract 23 Settlement of Forward Contracts 25 Futures Contract 27 Specification of a Futures Contract 29 Open Interest 32 Differences Between Forward and Futures Contracts 33 Pricing a Forward/Futures Contract 37 The Arbitrage Argument 39 Value of a Forward Contract 43 Convergence 45 Relationship of Futures Price and Expected Spot Price (SJ 47 Types of Futures Commodity Futures Introduction 57 Benefits of Commodity Futures 58 V vii Commodity Futures and Economy 59 Differences Commodity and Financial Futures 61 Futures Contract on Commodities 62 Pricing Commodity Futures 63 Hedging with Commodity Futures 64 Perfect and Imperfect Hedge 68 Basis and Basis Risk 71 Optimal Hedge Ratio 73 Hedging for Changes In Volume 2 77 Speculation with Commodity Futures 79 Spread Strategies with Futures 80 Hedging for Gross Profit Margin Stock and Index Futures 91 Introduction 91 Index Futures 92 Forward Contracts on Stocks 93 Futures Contract on Indices and Individual Stocks 95 Features and Specifications of Stock or Index Futures 97 Pricing Stock and Index Futures 99 Applications of Index Futures 102 Hedging Through Index Futures 102 Speculation with Stock Index Futures 114 Arbitrage with Stock Index Futures 115 Other Applications of Index Futures Currency Forwards and Futures 130 Introduction 130 Foreign Exchange Preliminaries 131 Foreign Exchange Risk 131 Foreign Exchange Markets 132 Foreign Exchange Rates 132

3 xiv Contents Currency Forwards 135 Foreign Exchange Transactions 135 Arbitrage and Foreign Exchange Rates 141 Hedging Through Forward Contracts 143 Speculation with Forward Contracts 148 Arbitrage with Forward Contract 150 Non-deliverable Forward (NDF) Contract 152 Features of NDFs 153 How NDF Works 154 NDF and Interest Rate Parity 154 Are NDFs Desirable 156 Currency Futures 156 Contract Specifications 157 Pricing Currency Futures/Forwards 160 Hedging Through Currency Futures 163 Speculation With Currency Futures 166 Arbitrage With Currency Futures 166 '> 6. Interest Rate Forwards and Futures 176 Introduction 176 Forward Rate Agreements (FRAs) 177 FRA-The Product 177 Hedging with FRA 184 Speculation with FRAs 187 Arbitrage with FRAs 187 Interest Rate Futures on T-bills 188 Futures Contracts on T-bills 188 Hedging with T-bill Futures 192 Speculation with T-bill Futures 197 Arbitrage with T-bill Futures 198 Eurodollar Futures 202 Eurodollars 202 Futures Contracts on Eurodollars 203 Pricing of and Hedging with Eurodollar Futures 204 Treasury Bond Futures 206 Pricing T-bonds 207 Futures Contract on T-bonds 208 Pricing of T-bond Futures 209 Hedging Principle 214 Duration and Modified Duration 215 Interest Rate Futures in India Interest Rate and Currency Swaps 231 Introduction 231 Interest Rate Swaps 232 Features of Swap 233 Need of Swap Intermediary The Swap Dealer/Bank 235 Applications of Swaps 237 Rationale for Swap The Comparative Advantage 242 Types of Interest Rate Swaps 244 Currency Swaps 245 Valuation of Swaps 252 Valuing Interest Rate Swap 253 Swap Quotes and Initial Pricing 258 Counterparty Risk and Swaps 261 Valuing Currency Swaps 263 Other Swaps 268 Commodity Swaps 268 Equity Swaps Options Basics 277 Introduction 277 Terminology of Options 278 Call Option 279 Put Option 280 Moneyness of Options 283 Types of Options 284 Understanding Options Quotations 286 Trading and Settlement 288

4 Contents xv Margins in Options 290 Adjustment For Corporate Actions on Stock Options 290 Options Other Than Stocks/Indices 292 Differences Between Options and Forwards/Futures Options Sensitivities 387 Introduction 387 Delta and Delta Hedging 388 Theta 400 Gamma and Gamma Neutrality 404 Other Greeks Option Pricing! 300 Introduction 300 Intrinsic Value and Time Value 301 Boundary Conditions for Option Pricing 303 Arbitrage-based Relationship of Option Pricing 310 Put Call Parity Option Pricing-H 326 Introduction 326 Binomial Option Pricing Model 327 Risk'Neutral Valuation 331 Equivalent Portfolio Approach for Option Valuation 334 Binomial Model for Put Pricing 336 Multi-Period Binomial Model 337 Valuing American Options 340 Binomial Model for Currency Options 348 Binomial Model for Index Options 349 Applying Binomial Model: Constructing Binomial Tree 350 Factors Affecting the Option Price 351 Black-Scholes Option Pricing Model 355 Assumptions of the Black-Scholes Model 364 Interpreting the Black-Scholes Model 365 Put Pricing Using the BSM 366 Volatility 371 Measuring Historical Volatility 372 Implied Volatility Options Applications 421 Introduction 421 Hedging Strategies with Options 422 Hedging with Stock Options 424 Hedging with Index Options 429 Hedging with Currency Options 433 Income Generation with Options 439 Option Trading Strategies Combination of Options 443 Straddle Long and Short 444 Strangle Long and Short 446 Straps and Strips 449 Bull Spread 450 Bear Spread 452 Butterfly Spread 454 Condor Spread 456 Calendar Spreads 458 Diagonal Spreads 459 Box Spread 460 Factors Affecting the Spreads 462 Synthesizing Instruments and Positions 463 Synthetic Long Position in Stock 463 Synthetic Short Position in Stock 464 Other Synthetic Positions Exotic Options Introduction 480 Forward Start Option

5 xvi Contents Binary or Digital Option 483 Chooser Option 485 Shout Option 486 Barrier Options 487 Asian Options 494 Other Exotics Credit Derivatives 507 Introduction 507 Credit derivative 508 Types of Credit Risks 509 Assessing Credit Risk: the Probability of Default 511 Credit Default Swaps 511 Total Return Swap 515 Credit Linked Notes 517 Collateralized Debt Obligations Other Derivatives 524 Introduction 524 Futures Options 524 Payoff of Options on Futures 525 Binomial Model For Futures Options 527 Valuation of Futures Options Black's Model 529 Interest Rate Options 530 Cap 531 Floor 536 Collar 539 " Options on Bonds 542 Option on Swaps Swaptions 545 Weather Derivatives 552 Energy Derivatives Accounting for Derivatives 565 Introduction 565 Accounting Definition of Derivatives 566 Types of Financial Instruments 567 Fair Value 569 Hedge Accounting 571 Accounting for Derivatives 577 In Conclusion 583 Area under the Standard Normal Distribution, N(d), for Values ofd < 486 Index 488

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