Fixed income securities: valuation, risk and risk management

Table of content:
Preface to the Adapted Edition

Preface

Acknowledgments

Part I Fixed Income Markets

1 An Introduction to Fixed Income Markets

1.1 Introduction

1.2 The Government Debt Markets

1.3 The Money Market

1.4 The Repo Market

1.5 The Mortgage-Backed Securities Market and Asset-Backed Securities Market

1.6 The Derivatives Market

1.7 Roadmap of Future Chapters

1.8 Summary

2 Basics of Fixed Income Securities

2.1 Discount Factors

2.2 Interest Rates

2.3 The Term Structure of Interest Rates

2.4 Coupon Bonds

2.5 Floating Rate Bonds

2.6 Summary

2.7 Exercises

2.8 Case Study: Orange County Inverse Floaters

2.9 Appendix: Extracting the Discount Factors Z (0, T)

3 Basics of Interest Rate Risk Management

3.1 The Variation in Interest Rates

3.2 Duration

3.3 Interest Rate Risk Management

3.4 Asset-Liability Management

3.5 Summary

3.6 Exercises

3.7 Case Study: The 1994 Bankruptcy of Orange County

3.8 Case Analysis: The Ex-Ante Risk in Orange County’s Portfolio

3.9 Appendix: Expected Shortfall under the Normal Distribution

4. Basic Refinements in Interest Rate Risk Management

4.1 Convexity

4.2 Slope and Curvature

4.3 Summary

4.4 Exercises

4.5 Case Study: Factor Structure in Orange County’s Portfolio

4.6 Appendix: Principal Component Analysis

5 Interest Rate Derivatives: Forwards and Swaps

5.1 Forward Rates and Forward Discount Factors

5.2 Forward Rate Agreements

5.3 Forward Contracts

5.4 Interest Rate Swaps

5.5 Interest Rate Risk Management using Derivative Securities

5.6 Summary

5.7 Exercises

5.8 Case Study: PiVe Capital Swap Spread Trades

6 Interest Rate Derivatives: Futures and Options

6.1 Interest Rate Futures

6.2 Options

6.3 Summary

6.4 Exercises

6.5 Appendix: Liquidity and the LIBOR Curve

6.6 Appendix: Transitioning from LIBOR to SOFR

7. Inflation, Monetary Policy, and the Federal Funds Rate

7.1 Central Banks

7.2 The RBI and Monetary Policy

7.3 Understanding the Term Structure of Interest Rates

7.4 Coping with Inflation Risk: Treasury Inflation-Protected Securities

7.5 Summary

7.6 Exercises

7.7 Case Study: Monetary Policy during the Subprime Crisis of 2007 – 2008

7.8 Appendix: Derivation of Expected Return Relation

8 Basics of Residential Mortgage-Backed Securities

8.1 Securitization

8.2 Mortgages and the Prepayment Option

8.3 Mortgage-Backed Securities

8.4 Collateralized Mortgage Obligations

8.5 Summary

8.6 Exercises

8.7 Case Study: PiVe Investment Group and the Hedging of Pass-

8.8 Appendix: Effective Convexity

Part II Term Structure Models: Trees

9 One Step Binomial Trees

9.1 A one-step interest rate binomial tree

9.2 No Arbitrage on a Binomial Tree

9.3 Derivative Pricing as Present Discounted Values of Future Cash

9.4 Risk Neutral Pricing

9.5 Summary

9.6 Exercises

10 Multi-Step Binomial Trees

10.1 A Two-Step Binomial Tree

10.2 Risk Neutral Pricing

10.3 Matching the Term Structure

10.4 Multi-step Trees

10.5 Pricing and Risk Assessment: The Spot Rate Duration

10.6 Summary

10.7 Exercises

11 Risk Neutral Trees and Derivative Pricing

11.1 Risk Neutral Trees

11.2 Using Risk Neutral Trees

11.3 Implied Volatilities and the Black, Derman, and Toy Model

11.4 Risk Neutral Trees for Futures Prices

11.5 Implied Trees: Final Remarks

11.6 Summary

11.7 Exercises



12 American Options

12.1 Callable Bonds

12.2 American Swaptions

12.3 Mortgages and Residential Mortgage-Backed Securities

12.4 Summary

12.5 Exercises

13 Monte Carlo Simulations on Trees

13.1 Monte Carlo Simulations on a One-step Binomial Tree

13.2 Monte Carlo Simulations on a Two-Step Binomial Tree

13.3 Monte Carlo Simulations on Multi-Step Binomial Trees

13.4 Pricing Path Dependent Options

13.5 Spot Rate Duration by Monte Carlo Simulations

13.6 Pricing Residential Mortgage-Backed Securities

13.7 Summary

13.8 Exercises

Part III Term Structure Models: Continuous Time

14 Interest Rate Models in Continuous Time

14.1 Brownian Motions

14.2 Differential Equations

14.3 Continuous Time Stochastic Processes

14.4 Ito’s Lemma

14.5 Illustrative Examples

14.6 Summary

14.7 Exercises

14.8 Appendix: Rules of Stochastic Calculus

15 No Arbitrage and The Pricing of Interest Rate Securities

15.1 Bond Pricing with Deterministic Interest Rate

15.2 Interest Rate Security Pricing in the Vasicek Model

15.3 Derivative Security Pricing

15.4 No Arbitrage Pricing in a General Interest Rate Model

15.5 Summary

15.6 Exercises

15.7 Appendix: Derivations

16 Dynamic Hedging and Relative Value Trades

16.1 The Replicating Portfolio

16.2 Rebalancing

16.3 Application 1: Relative Value Trades on the Yield Curve

16.4 Application 2: Hedging Derivative Exposure

16.5 The Theta - Gamma Relation

16.6 Summary

16.7 Exercises

16.8 Case Study: Relative Value Trades on the Yield Curve

16.9 Appendix: Derivation of Delta for Call Options

17 Risk Neutral Pricing and Monte Carlo Simulations

17.1 Risk Neutral Pricing

17.2 Feynman-Kac Theorem

17.3 Application of Risk Neutral Pricing: Monte Carlo Simulations

17.4 Example: Pricing a Range Floater

17.5 Hedging with Monte Carlo Simulations

17.6 Convexity by Monte Carlo Simulations

17.7 Summary

17.8 Exercises

17.9 Case Study: Procter & Gamble / Bankers Trust Leveraged Swap

18 The Risk and Return of Interest Rate Securities

18.1 Expected Return and the Market Price Risk

18.2 Risk Analysis: Risk Natural Monte Carlo Simulations

18.3 A Macroeconomic Model of the Term Structure

18.4 Case Analysis: The Risk in the P&G Leveraged Swap

18.5 Summary

18.6 Exercises

18.7 Appendix: Proof of Pricing Formula in Macroeconomic Model

19 No Arbitrage Models and Standard Derivatives

19.1 No Arbitrage Models

19.2 The Ho-Lee Model Revisited

19.3 The Hull-White Model

19.4 Standard Derivatives under the “Normal” Model

19.5 The “Lognormal” Model

19.6 Generalized Affine Term Structure Models

19.7 Summary

19.8 Exercises

19.9 Appendix: Proofs



20 The Market Model for Standard Derivatives and Options’ Volatility Dynamics

20.1 The Black Formula for Caps and Floors Pricing

20.2 The Black Formula for Swaption Pricing

20.3 Summary

20.4 Exercises

21 Forward Risk Neutral Pricing and The Libor Market Model

21.1 One Difficulty with Risk Neutral Pricing

21.2 Change of Numeraire and the Forward Risk Neutral Dynamics

21.3 The Option Pricing Formula in “Normal” Models

21.4 The LIBOR Market Model

21.5 Forward Risk Neutral Pricing and the Black Formula for Swaptions

21.6 The Heath, Jarrow, and Morton Framework

21.7 Unnatural Lag and Convexity Adjustment

21.8 Summary

21.9 Exercises

21.10 Appendix: Derivations

22 Multifactor Models

22.1 Multifactor Ito’s Lemma with Independent Factors

22.2 No Arbitrage with Independent Factors

22.3 Correlated Factors

22.4 The Feynman-Kac Theorem

22.5 Forward Risk Neutral Pricing

22.6 The Multifactor LIBOR Market Model

22.7 Affine and Quadratic Term Structure Models

22.8 Summary

22.9 Exercises

22.10 Appendix

References

Index
[https://www.wileyindia.com/fixed-income-securities-valuation-risk-and-risk-management-an-indian-adaptation.html]

Fixed Income Securities: Valuation, Risk, and Risk Management, 1st Edition provides a thorough discussion of the world of fixed income securities, the forces affecting their prices, their risks, and the

appropriate risk management practices. This book, however, provides a methodology, and not a "shopping list" of all the possible interest rate securities that have ever been invented. It instead provides examples and methodologies that can be applied quite universally once the basic concepts have been understood.
(https://www.wileyindia.com/fixed-income-securities-valuation-risk-and-risk-management-an-indian-adaptation.html)