Exam 26: Modeling Term Structure Movements

A $100 face value one-year risk-free discount bond is priced at $95. The two-year discount bond is priced at $90. After one year, the two-year bond will be worth either $91 or $97. The probability of this bond moving to a price of $97 is

A $100 face value one-year risk-free discount bond is priced at $95. The two-year discount bond is priced at $90. After one year, the two-year bond will take one of three equiprobable prices, spaced $5 apart. The middle value of these possible prices is

A $100 face value one-year risk-free discount bond is priced at $95. After one year, the two-year bond will be worth either $91 or $97. What (rounded to the nearest dollar) is the highest possible price of the two-year bond that is arbitrage-free?

If we use the Black-Scholes model for bond options, then we assume that bond prices are lognormal, as the underlying asset in the Black-Scholes model is assumed to have a lognormal distribution. Which of the following is not a consequence of this assumption?

The term "no-arbitrage" class of term-structure models refers to

In the Black-Scholes formula, interest rates are assumed to be constant. This is not appropriate for pricing options on bonds primarily because

Suppose that the one-year and two-year zero-coupon rates are 6% and 7%, respectively (assume continuous compounding). After one year, let the one-year zero-coupon rate move down to 4% or up to 9%. What must be the probability of the up move for the rates to be arbitrage-free?

In the Black-Scholes framework, return volatility is assumed to be constant over the life of the option. This is not theoretically appropriate for pricing options on (default-risk-free) bonds because

"Equilibrium" models of the term-structure

Which of the following is not sufficient for a pricing tree for risky bonds to be free of arbitrage?

"No-arbitrage" models of the interest rate differ from "equilibrium" models of the interest rate in that

Which of the following statements is implied by the existence of no-arbitrage in a risk-neutral pricing framework?

Suppose that the one-year and two-year zero-coupon rates are 6% and 7%, respectively (assume continuous compounding). After one year, let the one-year zero-coupon rates move down to $r _ { d }$ or up to $r _ { u } = 1.2 r _ { d }$ , with equal probability. The rate $r _ { u }$ that is arbitrage-free under these conditions is

A $100 face value one-year risk-free discount bond is priced at $95. The two-year discount bond is priced at $90. After one year, the two-year bond will take one of three possible prices with defined probabilities. Which of the following sets of prices is acceptable from a no-arbitrage standpoint?