Chapter 12: Valuation of investments (2)

Question 1

Interest rate derivatives are more difficult to value than equity derivatives, since: (4)

Answer 1

1. the behavoiur of an individual interest rate is more complicated than that of a stock price.
2. for the valuation of many products, it is necessary to develop a model describing the behaviour of the entire yield curve.
3. the volatilities of different points on the yield curve are different.
4. interest rates are used for discounting as well as for determining payoffs from the derivative.

Question 2

Interest rate cap

Answer 2

Interest rate cap is an interest rate option, which is designed to provide insurance against the rate of interest on an underlying note rising above a certain level.

This is known as the cap rate

Question 3

Interest rate floor

Answer 3

An interest rate floor contract provides a payoff when the interest rate on an underlying Floating Rate Note falls below a certain rate.

Question 4

Interest rate cap payoff at time t(k+1)

Answer 4

L * S(k) * max(R(k) - R(x),0)

Where:
R(x) - is the interest rate cap

Question 5

Interest rate floor payoff at time t(k+1)

Answer 5

L * S(k) * max(R(x) - R(k),0)

Where:
R(x) - is the interest rate floor

Question 6

The relationship between caps and floors: put-call parity

Answer 6

cap price = floor price + value of swap

where the swap entails receiving the floating rate and paying a fixed rate.

Question 7

Swaption in relation to a bond

Answer 7

A swaption can be regarded as an option to exchange a fixed rate bond for the principal amount of the swap.

Question 8

Swaption - put

Answer 8

If the swaption gives the holder the right to pay fixed and receive floating, it is a put option on a fixed rate bond with a strike price equal to the principal.

Question 9

Swap rate

Answer 9

The swap rate for a particular term at a particular time is the fixed interest rate that would be exchanged for LIBOR in a new swap with the same outstanding term.

Question 10

The evaluation of assets for securitisation will consider factors such as (5)

Answer 10

1. predictability and sustainability of adequate cashflows
2. lease terms
3. rental property
4. degree of potential competition
5. barriers to competitive entry

Question 11

For evaluation of a securitisation, the modelling of the cashflows will involve key features such as: (4)

Answer 11

1. statistics ( early repayment experience)
2. probability (default / recovery and timing)
3. treasury management (payments in / payments out)
4. structuring and security insurance

Question 12

Vanilla credit default swap (CDS)

Answer 12

The payoff per annum from a credit default swap is equal to the excess return on the bond over the risk-free rate.

Question 13

Value of a total return swap

Answer 13

The value of a total return swap is the difference between the values of the assets generating the returns on each side of the swap.

Question 14

Value of a credit spread option

Answer 14

The value of a credit spread option can be derived from the difference between the market value of the bond and its value at the strike spread.

Question 15

Swaption

Answer 15

A swaption provides its holder with the right, but not the obligation, to enter into a swap agreement on specified terms on a fixed strike date.

Question 16

The approximations implied by Black’s model for valuing a European bond options: (2)

Answer 16

1. The expected value of V(T) is assumed equal to its forward price F(0).
2. The stochastic behaviour of interest rates is not taken into account in the way the discounting is done.

** It can be shown, however, that these two assumptions have exactly offsetting effects.