Pre-Break. The focus in the class since the Christmas break has been on modeling the term structure. At this point, you should have a deep intuitive understanding of the following models: Vasicek (1-factor Gaussian) Model CIR 1-factor CIR 2-factor Black-Derman-Toy ("Arbitrage-Free Model") Examples of questions that you should be able to answer: 1) Show the basic pricing relationship between the path of the short-rate and the price of a zero-coupon bond. Note that this pricing relationship is always true (it does not depend on the model assumptions.) -- Similarly show the basic pricing equation for a Call Option on a zero-coupon bond. 2) What is the difference between the 1-factor CIR model and the Vasicek model? a) How do the assumptions differ? Which assumptions are more reasonable? (Be sure to include how risk is han b) How do the implications for zero-coupon bonds (I.e., the term structure) differ? 3) What are the advantages of the 2-factor CIR model, relative to the 1-factor model (in terms of each model's flexib 4) The shape of the yield curve depends on three things: a) Expectations b) Risk c) Convexity Explain each of these three effects in terms of: a) the basic pricing relationship. b) the Vasicek model. c) the CIR 1-factor model. d) the 2-factor CIR model. 5) What is an "arbitrage-free model" (e.g., Black, Derman, Toy), and how does it differ from a structural model (e.g. 6) Explain how the Black, Derman, Toy model is used to build the pricing tree. Be sure to include where you would to the model. Also at this point, you should be able to build the pricing tree in the BDT model. Here is a sample problem: Black Derman Toy Model Assume the following initial term structure and volatility information YTM (%) Volatility Maturity Of Yields (%) (Years) 0.1 1 0.11 0.19 2 0.12 0.18 3 0.125 0.17 4 0.13 0.16 5 The risk-neutral probability of going up is 50%. Assume that 1 period is 1 year. Construct the Black-Derman-Toy short rate tree consistent with given data. From the first half of the class, you should be able to provide intuition about investment strategies that relate to the numerical q Examples: 1) Why might the holding-period return on an investment differ from the yield-to-maturity that prevailed on the invest a) when you hold the instrument to maturity. b) when you sell the instrument before maturity. ---Explain how your answers to the previous questions relate to the concept of duration. 2) Explain the formation of the BBA portfolio in Bloomberg. Under what conditions would you advise a trader to long (short) this position? 3) Explain the convexity of a CMO tranche. Under what conditions would you advise a trader to long (short) the various tranches in a CMO. 4) Explain how a PAC mortgage-backed security works. 5) Under what future scenarios will a TIPS have a better holding-period return than an otherwise identical T-Bond? ---Under what future scenarios will a TIPS have a worse holding-period return than an otherwise identical T-Bond? wing models: a zero-coupon bond. he model assumptions.) e to include how risk is handled in each model.) erms of each model's flexibility in describing different yield curve shapes). om a structural model (e.g., Vasicek, CIR)? o include where you would obtain the needed inputs a sample problem: at relate to the numerical questions from the take-home mid-term. hat prevailed on the investment when it was purchased? herwise identical T-Bond? herwise identical T-Bond?