Preface |
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xv | |
About the Companion Website |
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xix | |
Part I Overview |
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1 Financial Markets: Functions, Institutions, and Traded Assets |
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1 | (66) |
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1.1 What is the purpose of finance? |
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2 | (10) |
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12 | (34) |
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15 | (5) |
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1.2.2 Assets vs. securities |
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20 | (2) |
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22 | (2) |
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24 | (3) |
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27 | (2) |
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29 | (17) |
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1.3 Market participants and their roles |
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46 | (7) |
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1.3.1 Commercial vs. investment banks |
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48 | (1) |
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1.3.2 Investment funds and insurance companies |
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49 | (2) |
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1.3.3 Dealers and brokers |
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51 | (1) |
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1.3.4 Hedgers, speculators, and arbitrageurs |
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51 | (2) |
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1.4 Market structure and trading strategies |
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53 | (7) |
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1.4.1 Primary and secondary markets |
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53 | (1) |
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1.4.2 Over-the-counter vs. exchange-traded derivatives |
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53 | (1) |
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1.4.3 Auction mechanisms and the limit order book |
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53 | (2) |
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1.4.4 Buying on margin and leverage |
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55 | (3) |
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58 | (2) |
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60 | (3) |
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63 | (2) |
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65 | (1) |
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65 | (2) |
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Problems in Quantitative Finance |
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67 | (1) |
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2.1 Portfolio optimization |
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68 | (12) |
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2.1.1 Static portfolio optimization: Mean-variance efficiency |
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70 | (5) |
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2.1.2 Dynamic decision-making under uncertainty: A stylized consumption-saving model |
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75 | (5) |
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2.2 Risk measurement and management |
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80 | (22) |
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2.2.1 Sensitivity of asset prices to underlying risk factors |
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81 | (3) |
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2.2.2 Risk measures in a non-normal world: Value-at-risk |
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84 | (9) |
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2.2.3 Risk management: Introductory hedging examples |
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93 | (7) |
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2.2.4 Financial vs. nonfinancial risk factors |
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100 | (2) |
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2.3 The no-arbitrage principle in asset pricing |
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102 | (15) |
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2.3.1 Why do we need asset pricing models? |
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103 | (1) |
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2.3.2 Arbitrage strategies |
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104 | (4) |
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2.3.3 Pricing by no-arbitrage |
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108 | (4) |
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2.3.4 Option pricing in a binomial model |
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112 | (4) |
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2.3.5 The limitations of the no-arbitrage principle |
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116 | (1) |
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2.4 The mathematics of arbitrage |
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117 | (12) |
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2.4.1 Linearity of the pricing functional and law of one price |
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119 | (1) |
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2.4.2 Dominant strategies |
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120 | (5) |
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2.4.3 No-arbitrage principle and risk-neutral measures |
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125 | (4) |
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S2.1 Multiobjective optimization |
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129 | (4) |
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S2.2 Summary of LP duality |
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133 | (4) |
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137 | (2) |
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139 | (1) |
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139 | (4) |
Part II Fixed-income assets |
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3 Elementary Theory of Interest Rates |
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143 | (64) |
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3.1 The time value of money: Shifting money forward in time |
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146 | (7) |
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3.1.1 Simple vs. compounded rates |
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147 | (3) |
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3.1.2 Quoted vs. effective rates: Compounding frequencies |
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150 | (3) |
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3.2 The time value of money: Shifting money backward in time |
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153 | (8) |
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3.2.1 Discount factors and pricing a zero-coupon bond |
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154 | (4) |
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3.2.2 Discount factors vs. interest rates |
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158 | (3) |
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3.3 Nominal vs. real interest rates |
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161 | (2) |
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3.4 The term structure of interest rates |
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163 | (2) |
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3.5 Elementary bond pricing |
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165 | (25) |
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3.5.1 Pricing coupon-bearing bonds |
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165 | (3) |
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3.5.2 From bond prices to term structures, and vice versa |
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168 | (3) |
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3.5.3 What is a risk-free rate, anyway? |
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171 | (3) |
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174 | (6) |
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180 | (8) |
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3.5.6 Pricing floating rate bonds |
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188 | (2) |
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3.6 A digression: Elementary investment analysis |
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190 | (3) |
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191 | (1) |
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3.6.2 Internal rate of return |
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192 | (1) |
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193 | (1) |
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3.7 Spot vs. forward interest rates |
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193 | (10) |
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3.7.1 The forward and the spot rate curves |
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197 | (1) |
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3.7.2 Discretely compounded forward rates |
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197 | (1) |
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3.7.3 Forward discount factors |
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198 | (1) |
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3.7.4 The expectation hypothesis |
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199 | (3) |
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3.7.5 A word of caution: Model risk and hidden assumptions |
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202 | (1) |
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S3.1 Proof of Equation (3.42) |
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203 | (1) |
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203 | (2) |
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205 | (1) |
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205 | (2) |
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4 Forward Rate Agreements, Interest Rate Futures, and Vanilla Swaps |
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207 | (22) |
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4.1 LIBOR and EURIBOR rates |
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208 | (1) |
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4.2 Forward rate agreements |
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209 | (7) |
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4.2.1 A hedging view of forward rates |
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210 | (4) |
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4.2.2 FRAs as bond trades |
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214 | (1) |
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4.2.3 A numerical example |
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215 | (1) |
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216 | (4) |
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4.4 Vanilla interest rate swaps |
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220 | (6) |
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4.4.1 Swap valuation: Approach 1 |
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221 | (2) |
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4.4.2 Swap valuation: Approach 2 |
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223 | (2) |
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4.4.3 The swap curve and the term structure |
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225 | (1) |
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226 | (1) |
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226 | (1) |
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226 | (3) |
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229 | (18) |
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5.1 Day count conventions |
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230 | (1) |
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231 | (6) |
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5.2.1 Bond credit ratings |
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233 | (1) |
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5.2.2 Quoting bond prices |
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233 | (2) |
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5.2.3 Bonds with embedded options |
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235 | (2) |
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5.3 Interest rate derivatives |
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237 | (2) |
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237 | (1) |
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5.3.2 Bond futures and options |
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238 | (1) |
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5.4 The repo market and other money market instruments |
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239 | (1) |
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240 | (4) |
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244 | (1) |
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244 | (1) |
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244 | (3) |
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6 Interest Rate Risk Management |
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247 | (30) |
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6.1 Duration as a first-order sensitivity measure |
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248 | (9) |
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6.1.1 Duration of fixed-coupon bonds |
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250 | (4) |
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6.1.2 Duration of a floater |
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254 | (1) |
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6.1.3 Dollar duration and interest rate swaps |
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255 | (2) |
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6.2 Further interpretations of duration |
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257 | (4) |
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6.2.1 Duration and investment horizons |
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258 | (2) |
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6.2.2 Duration and yield volatility |
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260 | (1) |
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6.2.3 Duration and quantile-based risk measures |
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260 | (1) |
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6.3 Classical duration-based immunization |
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261 | (4) |
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262 | (1) |
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263 | (2) |
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6.4 Immunization by interest rate derivatives |
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265 | (1) |
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6.4.1 Using interest rate swaps in asset-liability management |
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266 | (1) |
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6.5 A second-order refinement: Convexity |
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266 | (3) |
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6.6 Multifactor models in interest rate risk management |
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269 | (2) |
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271 | (1) |
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272 | (1) |
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273 | (4) |
Part III Equity portfolios |
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7 Decision-Making under Uncertainty: The Static Case |
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277 | (42) |
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7.1 Introductory examples |
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278 | (4) |
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7.2 Should we just consider expected values of returns and monetary outcomes? |
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282 | (6) |
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7.2.1 Formalizing static decision-making under uncertainty |
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283 | (1) |
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7.2.2 The flaw of averages |
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284 | (4) |
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7.3 A conceptual tool: The utility function |
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288 | (11) |
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7.3.1 A few standard utility functions |
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293 | (4) |
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7.3.2 Limitations of utility functions |
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297 | (2) |
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299 | (11) |
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7.4.1 Coherent risk measures |
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300 | (2) |
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7.4.2 Standard deviation and variance as risk measures |
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302 | (1) |
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7.4.3 Quantile-based risk measures: VOR and CV@R |
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303 | (6) |
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7.4.4 Formulation of mean-risk models |
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309 | (1) |
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310 | (4) |
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314 | (1) |
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S7.1.1 Proof of Theorem 7.2 |
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314 | (1) |
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S7.1.2 Proof of Theorem 7.4 |
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315 | (1) |
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315 | (2) |
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317 | (1) |
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317 | (2) |
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8 Mean-Variance Efficient Portfolios |
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319 | (32) |
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8.1 Risk aversion and capital allocation to risky assets |
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320 | (5) |
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8.1.1 The role of risk aversion |
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324 | (1) |
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8.2 The mean-variance efficient frontier with risky assets |
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325 | (7) |
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8.2.1 Diversification and portfolio risk |
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325 | (1) |
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8.2.2 The efficient frontier in the case of two risky assets |
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326 | (3) |
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8.2.3 The efficient frontier in the case of n risky assets |
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329 | (3) |
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8.3 Mean-variance efficiency with a risk-free asset: The separation property |
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332 | (5) |
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8.4 Maximizing the Sharpe ratio |
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337 | (4) |
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8.4.1 Technical issues in Sharpe ratio maximization |
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340 | (1) |
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8.5 Mean-variance efficiency vs. expected utility |
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341 | (2) |
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8.6 Instability in mean-variance portfolio optimization |
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343 | (2) |
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S8.1 The attainable set for two risky assets is a hyperbola |
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345 | (1) |
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S8.2 Explicit solution of mean-variance optimization in matrix form |
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346 | (2) |
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348 | (1) |
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349 | (1) |
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349 | (2) |
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351 | (22) |
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9.1 Statistical issues in mean-variance portfolio optimization |
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352 | (1) |
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9.2 The single-index model |
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353 | (5) |
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9.2.1 Estimating a factor model |
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354 | (2) |
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9.2.2 Portfolio optimization within the single-index model |
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356 | (2) |
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9.3 The Treynor-Black model |
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358 | (7) |
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9.3.1 A top-down/bottom-up optimization procedure |
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362 | (3) |
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365 | (2) |
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9.5 Factor models in practice |
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367 | (1) |
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S9.1 Proof of Equation (9.17) |
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368 | (1) |
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369 | (2) |
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371 | (1) |
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371 | (2) |
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10 Equilibrium Models: CAPM and APT |
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373 | (44) |
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10.1 What is an equilibrium model? |
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374 | (1) |
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10.2 The capital asset pricing model |
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375 | (6) |
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10.2.1 Proof of the CAPM formula |
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377 | (1) |
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378 | (2) |
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10.2.3 CAPM as a pricing formula and its practical relevance |
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380 | (1) |
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10.3 The Black-Litterman portfolio optimization model |
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381 | (7) |
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10.3.1 Black-Litterman model: The role of CAPM and Bayesian Statistics |
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382 | (4) |
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10.3.2 Black-Litterman model: A numerical example |
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386 | (2) |
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10.4 Arbitrage pricing theory |
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388 | (10) |
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389 | (2) |
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10.4.2 A not-so-rigorous proof of APT |
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391 | (1) |
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10.4.3 APT for Well-Diversified Portfolios |
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392 | (1) |
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10.4.4 APT for Individual Assets |
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393 | (1) |
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10.4.5 Interpreting and using APT |
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394 | (4) |
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10.5 The behavioral critique |
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398 | (6) |
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10.5.1 The efficient market hypothesis |
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400 | (1) |
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10.5.2 The psychology of choice by agents with limited rationality |
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400 | (1) |
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10.5.3 Prospect theory: The aversion to sure loss |
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401 | (3) |
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S10.1 Bayesian statistics |
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404 | (7) |
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S10.1.1 Bayesian estimation |
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405 | (2) |
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S10.1.2 Bayesian learning in coin flipping |
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407 | (1) |
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S10.1.3 The expected value of a normal distribution |
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408 | (3) |
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411 | (2) |
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413 | (1) |
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413 | (4) |
Part IV Derivatives |
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11 Modeling Dynamic Uncertainty |
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417 | (64) |
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11.1 Stochastic processes |
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420 | (18) |
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11.1.1 Introductory examples |
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422 | (6) |
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11.1.2 Marginals do not tell the whole story |
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428 | (2) |
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11.1.3 Modeling information: Filtration generated by a stochastic process |
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430 | (3) |
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433 | (3) |
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436 | (2) |
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11.2 Stochastic processes in continuous time |
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438 | (3) |
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11.2.1 A fundamental building block: Standard Wiener process |
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438 | (2) |
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11.2.2 A generalization: Levy processes |
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440 | (1) |
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11.3 Stochastic differential equations |
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441 | (6) |
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11.3.1 A deterministic differential equation: The bank account process |
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442 | (1) |
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11.3.2 The generalized Wiener process |
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443 | (2) |
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11.3.3 Geometric Brownian motion and Ito processes |
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445 | (2) |
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11.4 Stochastic integration and Ito's lemma |
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447 | (10) |
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11.4.1 A digression: Riemann and Riemann-Stieltjes integrals |
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447 | (1) |
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11.4.2 Stochastic integral in the sense of Ito |
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448 | (5) |
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453 | (4) |
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11.5 Stochastic processes in financial modeling |
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457 | (5) |
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11.5.1 Geometric Brownian motion |
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457 | (3) |
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460 | (2) |
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11.6 Sample path generation |
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462 | (6) |
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11.6.1 Monte Carlo sampling |
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463 | (2) |
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465 | (3) |
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S11.1 Probability spaces, measurability, and information |
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468 | (8) |
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476 | (2) |
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478 | (1) |
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478 | (3) |
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12 Forward and Futures Contracts |
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481 | (24) |
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12.1 Pricing forward contracts on equity and foreign currencies |
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482 | (8) |
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12.1.1 The spot-forward parity theorem |
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482 | (3) |
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12.1.2 The spot-forward parity theorem with dividend income |
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485 | (2) |
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12.1.3 Forward contracts on currencies |
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487 | (2) |
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12.1.4 Forward contracts on commodities or energy: Contango and backwardation |
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489 | (1) |
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12.2 Forward vs. futures contracts |
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490 | (3) |
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12.3 Hedging with linear contracts |
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493 | (8) |
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12.3.1 Quantity-based hedging |
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493 | (1) |
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12.3.2 Basis risk and minimum variance hedging |
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494 | (2) |
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12.3.3 Hedging with index futures |
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496 | (3) |
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499 | (2) |
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501 | (1) |
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502 | (1) |
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502 | (3) |
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13 Option Pricing: Complete Markets |
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505 | (74) |
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506 | (4) |
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507 | (1) |
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508 | (2) |
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13.2 Model-free price restrictions |
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510 | (9) |
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13.2.1 Bounds on call option prices |
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511 | (3) |
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13.2.2 Bounds on put option prices: Early exercise and continuation regions |
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514 | (3) |
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13.2.3 Parity relationships |
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517 | (2) |
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13.3 Binomial option pricing |
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519 | (11) |
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13.3.1 A hedging argument |
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520 | (3) |
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13.3.2 Lattice calibration |
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523 | (1) |
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13.3.3 Generalization to multiple steps |
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524 | (3) |
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13.3.4 Binomial pricing of American-style options |
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527 | (3) |
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13.4 A continuous-time model: The Black-Scholes-Merton pricing formula |
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530 | (15) |
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13.4.1 The delta-hedging view |
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532 | (7) |
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13.4.2 The risk-neutral view: Feynman-Kac representation theorem |
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539 | (4) |
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13.4.3 Interpreting the factors in the BSM formula |
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543 | (2) |
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13.5 Option price sensitivities: The Greeks |
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545 | (8) |
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546 | (4) |
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550 | (1) |
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13.5.3 Relationship between delta, gamma, and theta |
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551 | (1) |
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552 | (1) |
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13.6 The role of volatility |
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553 | (3) |
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13.6.1 The implied volatility surface |
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553 | (2) |
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13.6.2 The impact of volatility on barrier options |
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555 | (1) |
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13.7 Options on assets providing income |
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556 | (6) |
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557 | (1) |
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558 | (1) |
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559 | (1) |
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13.7.4 The mechanics of futures options |
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559 | (1) |
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13.7.5 A binomial view of futures options |
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560 | (2) |
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13.7.6 A risk-neutral view of futures options |
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562 | (1) |
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13.8 Portfolio strategies based on options |
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562 | (7) |
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13.8.1 Portfolio insurance and the Black Monday of 1987 |
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563 | (1) |
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13.8.2 Volatility trading |
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564 | (2) |
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13.8.3 Dynamic vs. Static hedging |
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566 | (3) |
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13.9 Option pricing by numerical methods |
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569 | (1) |
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570 | (5) |
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575 | (1) |
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576 | (3) |
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14 Option Pricing: Incomplete Markets |
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579 | (38) |
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14.1 A PDE approach to incomplete markets |
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581 | (7) |
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14.1.1 Pricing a zero-coupon bond in a driftless world |
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584 | (4) |
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14.2 Pricing by short-rate models |
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588 | (7) |
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14.2.1 The Vasicek short-rate model |
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589 | (5) |
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14.2.2 The Cox-Ingersoll-Ross short-rate model |
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594 | (1) |
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14.3 A martingale approach to incomplete markets |
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595 | (8) |
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14.3.1 An informal approach to martingale equivalent measures |
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598 | (2) |
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14.3.2 Choice of numeraire: The bank account |
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600 | (1) |
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14.3.3 Choice of numeraire: The zero-coupon bond |
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601 | (1) |
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14.3.4 Pricing options with stochastic interest rates: Black's model |
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602 | (1) |
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603 | (9) |
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14.4 Issues in model calibration |
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603 | (1) |
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14.4.1 Bias-variance tradeoff and regularized least-squares |
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604 | (5) |
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14.4.2 Financial model calibration |
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609 | (3) |
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612 | (1) |
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612 | (5) |
Part V Advanced optimization models |
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15 Optimization Model Building |
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617 | (82) |
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15.1 Classification of optimization models |
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618 | (7) |
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625 | (3) |
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15.2.1 Cash flow matching |
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627 | (1) |
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15.3 Quadratic programming |
|
|
628 | (4) |
|
15.3.1 Maximizing the Sharpe ratio |
|
|
629 | (2) |
|
15.3.2 Quadratically constrained quadratic programming |
|
|
631 | (1) |
|
|
632 | (10) |
|
15.4.1 A MIQP model to minimize TEV under a cardinality constraint |
|
|
634 | (2) |
|
15.4.2 Good MILP model building: The role of tight model formulations |
|
|
636 | (6) |
|
|
642 | (13) |
|
|
644 | (6) |
|
15.5.2 Second-order cone programming |
|
|
650 | (3) |
|
15.5.3 Semidefinite programming |
|
|
653 | (2) |
|
15.6 Stochastic optimization |
|
|
655 | (20) |
|
15.6.1 Chance-constrained LP models |
|
|
656 | (1) |
|
15.6.2 Two-stage stochastic linear programming with recourse |
|
|
657 | (6) |
|
15.6.3 Multistage stochastic linear programming with recourse |
|
|
663 | (7) |
|
15.6.4 Scenario generation and stability in stochastic programming |
|
|
670 | (5) |
|
15.7 Stochastic dynamic programming |
|
|
675 | (7) |
|
15.7.1 The dynamic programming principle |
|
|
676 | (3) |
|
15.7.2 Solving Bellman's equation: The three curses of dimensionality |
|
|
679 | (1) |
|
15.7.3 Application to pricing options with early exercise features |
|
|
680 | (2) |
|
15.8 Decision rules for multistage SLPs |
|
|
682 | (4) |
|
15.9 Worst-case robust models |
|
|
686 | (5) |
|
15.9.1 Uncertain LPs: Polyhedral uncertainty |
|
|
689 | (1) |
|
15.9.2 Uncertain LPs: Ellipsoidal uncertainty |
|
|
690 | (1) |
|
15.10 Nonlinear programming models in finance |
|
|
691 | (2) |
|
15.10.1 Fixed-mix asset allocation |
|
|
692 | (1) |
|
|
693 | (2) |
|
|
695 | (1) |
|
|
696 | (3) |
|
16 Optimization Model Solving |
|
|
699 | (42) |
|
16.1 Local methods for nonlinear programming |
|
|
700 | (15) |
|
16.1.1 Unconstrained nonlinear programming |
|
|
700 | (3) |
|
16.1.2 Penalty function methods |
|
|
703 | (4) |
|
16.1.3 Lagrange multipliers and constraint qualification conditions |
|
|
707 | (6) |
|
|
713 | (2) |
|
16.2 Global methods for nonlinear programming |
|
|
715 | (4) |
|
16.2.1 Genetic algorithms |
|
|
716 | (1) |
|
16.2.2 Particle swarm optimization |
|
|
717 | (2) |
|
|
719 | (9) |
|
16.3.1 The simplex method |
|
|
720 | (3) |
|
16.3.2 Duality in linear programming |
|
|
723 | (3) |
|
16.3.3 Interior-point methods: Primal-dual barrier method for LP |
|
|
726 | (2) |
|
16.4 Conic duality and interior-point methods |
|
|
728 | (4) |
|
|
728 | (3) |
|
16.4.2 Interior-point methods for SOCP and SDP |
|
|
731 | (1) |
|
16.5 Branch-and-bound methods for integer programming |
|
|
732 | (4) |
|
16.5.1 A matheuristic approach: Fix-and-relax |
|
|
735 | (1) |
|
16.6 Optimization software |
|
|
736 | (3) |
|
|
737 | (1) |
|
16.6.2 Interfacing through imperative programming languages |
|
|
738 | (1) |
|
16.6.3 Interfacing through non-imperative algebraic languages |
|
|
738 | (1) |
|
16.6.4 Additional interfaces |
|
|
739 | (1) |
|
|
739 | (1) |
|
|
740 | (1) |
Bibliography |
|
741 | (2) |
Index |
|
743 | |