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Fall_2010_Midterm2_Solution_Key

# Fall_2010_Midterm2_Solution_Key - The Wharton School...

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1 The Wharton School University of Pennsylvania Prof. Stephan Dieckmann, Fall 2010 FNCE 235/725: Fixed Income Securities Midterm Exam 2 - November 30, 2010 – Solution Key Question 1: (21 points total) TRUE or FALSE? No explanation is required. A correct answer is awarded 3 points, a false answer with 0 points. a. Assume the Vasicek model is true. Parameter φ determines the degree of autocorrelation of short-term interest rates. As φ approaches one, the term structure of interest rates becomes flat, holding everything else constant. TRUE. As φ approaches one, the predicted future short term rate approaches r, and the variance of the prediction approaches zero. As the step size approaches zero, the short term rate becomes deterministic as the current level r, hence the term structure flat. b. Usually the yield on a callable bond exceeds the yield on a comparable non-callable bond. However, the yield till maturity will be equal for these two bonds if the term structure is flat. FALSE. Even with a flat term structure, callable bonds usually trade at a discount relative to non-callable bonds, and the yields are not equal. c. The delta of an inverse floater is usually larger than the delta of a regular floater, assuming both securities trade at par. TRUE. The delta of a regular floater, e.g with reference rate LIBOR, is small as interest rates periodically reset. However, the delta of the inverse floater mainly stems from the fixed rate component, e.g. 10% - LIBOR, leading to a delta larger. d. No-arbitrage models, in comparison to equilibrium models, are designed to be exactly consistent with today’s observed term structure. In fact, in a no-arbitrage model the term structure is an input to the model. TRUE, see lecture note on alternative term structure models. e. A long position in a cap with strike rate X, plus a short position in a floor with strike rate X, both having the same time to maturity and reference rate, equals the position of an interest rate swap from the perspective of the counterparty receiving fixed rate X and paying the reference rate.

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2 FALSE. Max(R-X,0) – Max(X-R,0) = -X + R. Hence, it equals the position of an interest rate swap from the perspective of the counterparty paying fixed rate X and receiving the reference rate.
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Fall_2010_Midterm2_Solution_Key - The Wharton School...

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