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Fixed Income Securities: Valuation, Risk, and Risk Management

Book Description

The deep understanding of the forces that affect the valuation, risk and return of fixed income securities and their derivatives has never been so important. As the world of fixed income securities becomes more complex, anybody who studies fixed income securities must be exposed more directly to this complexity. This book provides a thorough discussion of these complex securities, the forces affecting their prices, their risks, and of the appropriate risk management practices. Fixed Income Securities, however, provides a methodology, and not a shopping list. It provides instead examples and methodologies that can be applied quite universally, once the basic concepts have been understood.

Table of Contents

  1. Cover Page
  2. Title Page
  3. Copyright
  4. Dedication
  5. CONTENTS
  6. PREFACE
  7. Acknowledgments
  8. PART I: FIXED INCOME MARKETS
    1. CHAPTER 1: AN INTRODUCTION TO FIXED INCOME MARKETS
      1. 1.1 INTRODUCTION
      2. 1.2 THE GOVERNMENT DEBT MARKETS
      3. 1.3 THE MONEY MARKET
      4. 1.4 THE REPO MARKET
      5. 1.5 THE MORTGAGE BACKED SECURITIES MARKET AND ASSET-BACKED SECURITIES MARKET
      6. 1.6 THE DERIVATIVES MARKET
      7. 1.7 ROADMAP OF FUTURE CHAPTERS
      8. 1.8 SUMMARY
    2. CHAPTER 2: BASICS OF FIXED INCOME SECURITIES
      1. 2.1 DISCOUNT FACTORS
      2. 2.2 INTEREST RATES
      3. 2.3 THE TERM STRUCTURE OF INTEREST RATES
      4. 2.4 COUPON BONDS
      5. 2.5 FLOATING RATE BONDS
      6. 2.6 SUMMARY
      7. 2.7 EXERCISES
      8. 2.8 CASE STUDY: ORANGE COUNTY INVERSE FLOATERS
      9. 2.9 APPENDIX: EXTRACTING THE DISCOUNT FACTORS Z(0, T) FROM COUPON BONDS
    3. CHAPTER 3: BASICS OF INTEREST RATE RISK MANAGEMENT
      1. 3.1 THE VARIATION IN INTEREST RATES
      2. 3.2 DURATION
      3. 3.3 INTEREST RATE RISK MANAGEMENT
      4. 3.4 ASSET-LIABILITY MANAGEMENT
      5. 3.5 SUMMARY
      6. 3.6 EXERCISES
      7. 3.7 CASE STUDY: THE 1994 BANKRUPTCY OF ORANGE COUNTY
      8. 3.8 CASE ANALYSIS: THE EX-ANTE RISK IN ORANGE COUNTY’S PORTFOLIO
      9. 3.9 APPENDIX: EXPECTED SHORTFALL UNDER THE NORMAL DISTRIBUTION
    4. CHAPTER 4: BASIC REFINEMENTS IN INTEREST RATE RISK MANAGEMENT
      1. 4.1 CONVEXITY
      2. 4.2 SLOPE AND CURVATURE
      3. 4.3 SUMMARY
      4. 4.4 EXERCISES
      5. 4.5 CASE STUDY: FACTOR STRUCTURE IN ORANGE COUNTY’S PORTFOLIO
      6. 4.6 APPENDIX: PRINCIPAL COMPONENT ANALYSIS
    5. CHAPTER 5: INTEREST RATE DERIVATIVES: FORWARDS AND SWAPS
      1. 5.1 FORWARD RATES AND FORWARD DISCOUNT FACTORS
      2. 5.2 FORWARD RATE AGREEMENTS
      3. 5.3 FORWARD CONTRACTS
      4. 5.4 INTEREST RATE SWAPS
      5. 5.5 INTEREST RATE RISK MANAGEMENT USING DERIVATIVE SECURITIES
      6. 5.6 SUMMARY
      7. 5.7 EXERCISES
      8. 5.8 CASE STUDY: PIVE CAPITAL SWAP SPREAD TRADES
    6. CHAPTER 6: INTEREST RATE DERIVATIVES: FUTURES AND OPTIONS
      1. 6.1 INTEREST RATE FUTURES
      2. 6.2 OPTIONS
      3. 6.3 SUMMARY
      4. 6.4 EXERCISES
      5. 6.5 APPENDIX: LIQUIDITY AND THE LIBOR CURVE
    7. CHAPTER 7: INFLATION, MONETARY POLICY, AND THE FEDERAL FUNDS RATE
      1. 7.1 THE FEDERAL RESERVE
      2. 7.2 PREDICTING THE FUTURE FED FUNDS RATE
      3. 7.3 UNDERSTANDING THE TERM STRUCTURE OF INTEREST RATES
      4. 7.4 COPING WITH INFLATION RISK: TREASURY INFLATION-PROTECTED SECURITIES
      5. 7.5 SUMMARY
      6. 7.6 EXERCISES
      7. 7.7 CASE STUDY: MONETARY POLICY DURING THE SUBPRIME CRISIS OF 2007 - 2008
      8. 7.8 APPENDIX: DERIVATION OF EXPECTED RETURN RELATION
    8. CHAPTER 8: BASICS OF RESIDENTIAL MORTGAGE BACKED SECURITIES
      1. 8.1 SECURITIZATION
      2. 8.2 MORTGAGES AND THE PREPAYMENT OPTION
      3. 8.3 MORTGAGE BACKED SECURITIES
      4. 8.4 COLLATERALIZED MORTGAGE OBLIGATIONS
      5. 8.5 SUMMARY
      6. 8.6 EXERCISES
      7. 8.7 CASE STUDY: PiVe INVESTMENT GROUP AND THE HEDGING OF PASS-THROUGH SECURITIES
      8. 8.8 APPENDIX: EFFECTIVE CONVEXITY
  9. PART II: TERM STRUCTURE MODELS: TREES
    1. CHAPTER 9: ONE STEP BINOMIAL TREES
      1. 9.1 A ONE-STEP INTEREST RATE BINOMIAL TREE
      2. 9.2 NO ARBITRAGE ON A BINOMIAL TREE
      3. 9.3 DERIVATIVE PRICING AS PRESENT DISCOUNTED VALUES OF FUTURE CASH FLOWS
      4. 9.5 SUMMARY
      5. 9.6 EXERCISES
    2. CHAPTER 10: MULTI-STEP BINOMIAL TREES
      1. 10.1 A TWO-STEP BINOMIAL TREE
      2. 10.2 RISK NEUTRAL PRICING
      3. 10.3 MATCHING THE TERM STRUCTURE
      4. 10.4 MULTI-STEP TREES
      5. 10.5 PRICING AND RISK ASSESSMENT: THE SPOT RATE DURATION
      6. 10.6 SUMMARY
      7. 10.7 EXERCISES
    3. CHAPTER 11: RISK NEUTRAL TREES AND DERIVATIVE PRICING
      1. 11.1 RISK NEUTRAL TREES
      2. 11.2 USING RISK NEUTRAL TREES
      3. 11.3 IMPLIED VOLATILITIES AND THE BLACK, DERMAN, AND TOY MODEL
      4. 11.4 RISK NEUTRAL TREES FOR FUTURES PRICES
      5. 11.5 IMPLIED TREES: FINAL REMARKS
      6. 11.6 SUMMARY
      7. 11.7 EXERCISES
    4. CHAPTER 12: AMERICAN OPTIONS
      1. 12.1 CALLABLE BONDS
      2. 12.2 AMERICAN SWAPTIONS
      3. 12.3 MORTGAGES AND RESIDENTIAL MORTGAGE BACKED SECURITIES
      4. 12.4 SUMMARY
      5. 12.5 EXERCISES
    5. CHAPTER 13: MONTE CARLO SIMULATIONS ON TREES
      1. 13.1 MONTE CARLO SIMULATIONS ON A ONE-STEP BINOMIAL TREE
      2. 13.2 MONTE CARLO SIMULATIONS ON A TWO-STEP BINOMIAL TREE
      3. 13.3 MONTE CARLO SIMULATIONS ON MULTI-STEP BINOMIAL TREES
      4. 13.4 PRICING PATH DEPENDENT OPTIONS
      5. 13.5 SPOT RATE DURATION BY MONTE CARLO SIMULATIONS
      6. 13.6 PRICING RESIDENTIAL MORTGAGE BACKED SECURITIES
      7. 13.7 SUMMARY
      8. 13.8 EXERCISES
  10. PART III: TERM STRUCTURE MODELS: CONTINUOUS TIME
    1. CHAPTER 14: INTEREST RATE MODELS IN CONTINUOUS TIME
      1. 14.1 BROWNIAN MOTIONS
      2. 14.2 DIFFERENTIAL EQUATIONS
      3. 14.3 CONTINUOUS TIME STOCHASTIC PROCESSES
      4. 14.4 ITO’S LEMMA
      5. 14.5 ILLUSTRATIVE EXAMPLES
      6. 14.6 SUMMARY
      7. 14.7 EXERCISES
      8. 14.8 APPENDIX: RULES OF STOCHASTIC CALCULUS
    2. CHAPTER 15: NO ARBITRAGE AND THE PRICING OF INTEREST RATE SECURITIES
      1. 15.1 BOND PRICING WITH DETERMINISTIC INTEREST RATE
      2. 15.2 INTEREST RATE SECURITY PRICING IN THE VASICEK MODEL
      3. 15.3 DERIVATIVE SECURITY PRICING
      4. 15.4 NO ARBITRAGE PRICING IN A GENERAL INTEREST RATE MODEL
      5. 15.5 SUMMARY
      6. 15.6 EXERCISES
      7. 15.7 APPENDIX: DERIVATIONS
    3. CHAPTER 16: DYNAMIC HEDGING AND RELATIVE VALUE TRADES
      1. 16.1 THE REPLICATING PORTFOLIO
      2. 16.2 REBALANCING
      3. 16.3 APPLICATION 1: RELATIVE VALUE TRADES ON THE YIELD CURVE
      4. 16.4 APPLICATION 2: HEDGING DERIVATIVE EXPOSURE
      5. 16.5 THE THETA - GAMMA RELATION
      6. 16.6 SUMMARY
      7. 16.7 EXERCISES
      8. 16.8 CASE STUDY: RELATIVE VALUE TRADES ON THE YIELD CURVE
      9. 16.9 APPENDIX: DERIVATION OF DELTA FOR CALL OPTIONS
    4. CHAPTER 17: RISK NEUTRAL PRICING AND MONTE CARLO SIMULATIONS
      1. 17.1 RISK NEUTRAL PRICING
      2. 17.2 FEYNMAN-KAC THEOREM
      3. 17.3 APPLICATION OF RISK NEUTRAL PRICING: MONTE CARLO SIMULATIONS
      4. 17.4 EXAMPLE: PRICING A RANGE FLOATER
      5. 17.5 HEDGING WITH MONTE CARLO SIMULATIONS
      6. 17.6 CONVEXITY BY MONTE CARLO SIMULATIONS
      7. 17.7 SUMMARY
      8. 17.8 EXERCISES
      9. 17.9 CASE STUDY: PROCTER & GAMBLE / BANKERS TRUST LEVERAGED SWAP
    5. CHAPTER 18: THE RISK AND RETURN OF INTEREST RATE SECURITIES
      1. 18.1 EXPECTED RETURN AND THE MARKET PRICE RISK
      2. 18.2 RISK ANALYSIS: RISK NATURAL MONTE CARLO SIMULATIONS
      3. 18.3 A MACROECONOMIC MODEL OF THE TERM STRUCTURE
      4. 18.4 CASE ANALYSIS: THE RISK IN THE P&G LEVERAGED SWAP
      5. 18.5 SUMMARY
      6. 18.6 EXERCISES
      7. 18.7 APPENDIX: PROOF OF PRICING FORMULA IN MACROECONOMIC MODEL
    6. CHAPTER 19: NO ARBITRAGE MODELS AND STANDARD DERIVATIVES
      1. 19.1 NO ARBITRAGE MODELS
      2. 19.2 THE HO-LEE MODEL REVISITED
      3. 19.3 THE HULL-WHITE MODEL
      4. 19.4 STANDARD DERIVATIVES UNDER THE “NORMAL” MODEL
      5. 19.5 THE “LOGNORMAL” MODEL
      6. 19.6 GENERALIZED AFFINE TERM STRUCTURE MODELS
      7. 19.7 SUMMARY
      8. 19.8 EXERCISES
      9. 19.9 APPENDIX: PROOFS
    7. Chapter 20: THE MARKET MODEL FOR STANDARD DERIVATIVES AND OPTIONS’ VOLATILITY DYNAMICS
      1. 20.1 THE BLACK FORMULA FOR CAPS AND FLOORS PRICING
      2. 20.2 THE BLACK FORMULA FOR SWAPTION PRICING
      3. 20.3 SUMMARY
      4. 20.4 EXERCISES
    8. CHAPTER 21: FORWARD RISK NEUTRAL PRICING AND THE LIBOR MARKET MODEL
      1. 21.1 ONE DIFFICULTY WITH RISK NEUTRAL PRICING
      2. 21.2 CHANGE OF NUMERAIRE AND THE FORWARD RISK NEUTRAL DYNAMICS
      3. 21.3 THE OPTION PRICING FORMULA IN “NORMAL” MODELS
      4. 21.4 THE LIBOR MARKET MODEL
      5. 21.5 FORWARD RISK NEUTRAL PRICING AND THE BLACK FORMULA FOR SWAPTIONS
      6. 21.6 THE HEATH, JARROW, AND MORTON FRAMEWORK
      7. 21.7 UNNATURAL LAG AND CONVEXITY ADJUSTMENT
      8. 21.8 SUMMARY
      9. 21.9 EXERCISES
      10. 21.10 APPENDIX: DERIVATIONS
    9. CHAPTER 22: MULTIFACTOR MODELS
      1. 22.1 MULTIFACTOR ITO’S LEMMA WITH INDEPENDENT FACTORS
      2. 22.2 NO ARBITRAGE WITH INDEPENDENT FACTORS
      3. 22.3 CORRELATED FACTORS
      4. 22.4 THE FEYNMAN-KAC THEOREM
      5. 22.5 FORWARD RISK NEUTRAL PRICING
      6. 22.6 THE MULTIFACTOR LIBOR MARKET MODEL
      7. 22.7 AFFINE AND QUADRATIC TERM STRUCTURE MODELS
      8. 22.8 SUMMARY
      9. 22.9 EXERCISES
      10. 22.10 APPENDIX
  11. REFERENCES
  12. INDEX
  13. LIST OF FIGURES
  14. LIST OF TABLES