Lecture 3+4

Question 1

how do interest rates change over time

Answer 1

The movement of interest rates is initially stimulated by the central bank, due to the state of the economy

Question 2

how is risk evaluated when building interest rate trees

Answer 2

we describe interest rates under the risk neutral valuation
where it is assumed to be 0.5

Question 3

who is the creator of the term structure of interest rate models

Answer 3

ho and lee 1986

Question 4

define a callable bond

Answer 4

bonds that give the issuer the right to repurchase the contractual cash flows of the bond
callable bonds are cheaper and offer a higher yield

bond will be called when the continuation value is higher than the cost of calling the bond

Question 5

define a putable bond

Answer 5

bonds that give the bondholder the right under certain circumstances, to sell the bond back to the corporation
putable bonds are more expensive and offer a lower yield

Question 6

define a caplet

Answer 6

caplet is a call option on an interest rate
It pays off if the interest rates at expiry are higher than
the agreed strike rate

Question 7

what is the cap premium equal to

Answer 7

the sum of the premium for the separate caplets

Question 8

given an interest rate lattice how would the probability of the “up” state motivate a corporation to issue a callable bond

Answer 8

Callable bonds provide the issuer the option to repurchase the issue in order to look for cheaper financing, hence the issuer tends to develop incentives to exercise the option when the probability of the “up” state is small, favouring low interest rate regimes

Question 9

given an interest rate lattice how would the probability of the “up” state motivate a corporation to issue a putable bond

Answer 9

Putable bonds provide the investor the option to sell the issue back in order to look for more lucrative investments, hence the issuer tends to develop incentives to exercise the option when the probability of the “up” state is large, favouring high interest rate regimes.

Question 10

Explain how the price of a callable and a putable bond would differ from standard bonds without option features.

Answer 10

Callable bonds are cheaper compared to bond without option features.

putable bonds are more expensive compared to bond without option features.

Question 11

Define an interest rate cap

Answer 11

A European (American) interest rate cap is a series of
independent European (American) caplets (calls) which
mature on dates corresponding to future interest
payments

Question 12

define a floorlet

Answer 12

floorlet is a put option on an interest rate
It pays off if the interest rates at expiry are lower than the
agreed strike rate