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

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

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

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

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

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

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?

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

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?

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

"Equilibrium" models of the term-structure

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?