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.