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Lecture Notes in Finance 2 (MiQE/F, MSc course at UNISG) Paul Söderlind1 7 January 2017 1University of St. Gallen. Address: s/bf-HSG, Rosenbergstrasse 52, CH-9000 St. Gallen, Switzerland. E-mail: Paul.Soderlind@unisg.ch. Document name: Fin2MiQEFAll.TeX. Contents 15 Forwards and Futures 5 15.1 Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 15.2 Forward and Futures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 15.3 Appendix: Data Sources . . . . . . . . . . . . . . . . . . . . . . . . . . 14 16 Interest Rate Calculations 15 16.1 Zero Coupon (discount or bullet) Bonds . . . . . . . . . . . . . . . . . . 15 16.2 Forward Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 16.3 Coupon Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 16.4 Price and Yield to Maturity of Bond Portfolios . . . . . . . . . . . . . . . 31 16.5 Swap and Repo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 16.6 Estimating the Yield Curve . . . . . . . . . . . . . . . . . . . . . . . . . 36 16.7 Conventions on Important Markets . . . . . . . . . . . . . . . . . . . . 43 16.8 Other Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 16.9 Appendix: More on Forward Rates . . . . . . . . . . . . . . . . . . . . 50 16.10Appendix: More Details on Bond Conventions . . . . . . . . . . . . . . 53 17 Bond Portfolios and Hedging 58 17.1 Bond Hedging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 17.2 Duration: Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 17.3 Using Duration to Improve the Hedging of a Bond Portfolio . . . . . . . 66 17.4 Problems with Duration Hedging . . . . . . . . . . . . . . . . . . . . . . 71 18 Interest Rate Models 76 18.1 Empirical Properties of Yield Curves . . . . . . . . . . . . . . . . . . . . 76 18.2 Yield Curve Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 18.3 Interest Rates and Macroeconomics . . . . . . . . . . . . . . . . . . . . 86 1 18.4 Forecasting Interest Rates . . . . . . . . . . . . . . . . . . . . . . . . . . 93 18.5 Risk Premia on Fixed Income Markets . . . . . . . . . . . . . . . . . . . 94 19 Basic Properties of Options 98 19.1 Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 19.2 Introduction to Options . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 19.3 Put-Call Parity for European Options . . . . . . . . . . . . . . . . . . . . 113 19.4 Pricing Bounds and Convexity of Pricing Functions . . . . . . . . . . . . 116 19.5 Early Exercise of American Options . . . . . . . . . . . . . . . . . . . . 122 19.6 Appendix: Details on Early Exercise of American Options . . . . . . . . 123 19.7 Appendix: Put-Call Relation for American Options . . . . . . . . . . . . 128 20 The Binomial Option Pricing Model 131 20.1 Overview of Option Pricing . . . . . . . . . . . . . . . . . . . . . . . . . 131 20.2 The Basic Binomial Model . . . . . . . . . . . . . . . . . . . . . . . . . 131 20.3 Interpretation of the Risk Neutral Probabilities . . . . . . . . . . . . . . . 139 20.4 Numerical Applications of the Binomial Model 21 The Black-Scholes Model . . . . . . . . . . . . . . 140 153 21.1 The Black-Scholes Model . . . . . . . . . . . . . . . . . . . . . . . . . . 153 21.2 Convergence of the BOPM to Black-Scholes . . . . . . . . . . . . . . . . 159 21.3 Hedging an Option . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 21.4 Estimating Riskneutral Distributions . . . . . . . . . . . . . . . . . . . 172 21.5 Appendix: More Details on the Black-Scholes Model . . . . . . . . . . 175 21.6 Appendix: The Probabilities in the BOPM and Black-Scholes Model . . 178 21.7 Appendix: Statistical Tables 22 FX and Interest Rate Options . . . . . . . . . . . . . . . . . . . . . . . . 183 186 22.1 Forward Contract on a Currency . . . . . . . . . . . . . . . . . . . . . . 186 22.2 Summary of the Black-Scholes Model . . . . . . . . . . . . . . . . . . . 187 22.3 Hedging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 22.4 FX Options: Put or Call? . . . . . . . . . . . . . . . . . . . . . . . . . . 189 22.5 FX Options: Risk Reversals and Strangles . . . . . . . . . . . . . . . . . 191 22.6 FX Options: Implied Volatility for Different Deltas . . . . . . . . . . . . 195 22.7 Options on Interest Rates: Caps and Floors . . . . . . . . . . . . . . . . . 196 2 23 Trading Volatility 199 23.1 The Purpose of Trading Volatility . . . . . . . . . . . . . . . . . . . . . . 199 23.2 VIX and VIX Futures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 23.3 Variance and Volatility Swaps . . . . . . . . . . . . . . . . . . . . . . . 201 3 Warning: a few of the tables and figures are reused in later chapters. 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