Term Structure Models
Term Structure Models 1. Zero-coupon bond prices and yields 2. Vasicek model 3. Cox-Ingersoll-Ross model 4. Multifactor Cox-Ingersoll-Ross models 5. Affine models 6. Completely affine models 7. Bond risk premia 8. Inflation and nominal asset prices 1 Readings and References Back, chapter 17. Duffie, chapter 7. Vasicek, O., 1977, An equilibrium characterization of the term structure, Journal of Financial Economics 5, 177-188. Cox, J., J. Ingersoll, and S. Ross, 1985, A theory of the term structure of interest rates, Econometrica 53, 385-407. Longsta↵, F., and E. Schwartz, 1992, Interest rate volatility and the term structure: A two-factor general equilibrium model, Journal of Finance 47, 1259-1282. Duffie, D., and R. Kan, 1996, A yield-factor model of interest rates, Mathematical Finance 6, 379-406. Du↵ee, G., 2002, Term premia and interest rate forecasts in affine models, Journal of Finance 57, 405-443. Drechsler, I., A. Savov, and P. Schnabl, A Model of Monetary Policy and Risk Premia, Journal of Finance forthcoming. 2 Summary of the Continuous-Time Financial Market dS0,t dSk,t I Security prices satisfy = rt dt and =(µk,t δk,t) dt + σk,tdBt. S0,t Sk,t − I Given tight tr. strat. ⇡t and consumption ct, portfolio value Xt satisfies the WEE: dXt = rtXt dt + ⇡t(µt rt1) dt + ⇡tσt dBt ct dt. • − − No arbitrage if ⇡tσt =0then ⇡t(µt rt1) = 0 ✓t s.t. σt✓t = µt rt1 I ) − )9 − dXt = rtXt dt + ⇡tσt(✓t dt + dBt) ct dt. ) − t 1 t 2 d ✓ dBs ✓s ds ⇤ = = − 0 s0 −2 0 | | I Under emm ⇤ given by dP ZT where Zt e , P P t R R B = Bt + ✓s ds is Brownian motion.
[Show full text]