1. Multi-period Options Interest Rate Caps Interest Rate Floors
Interest Rate Collars
Captions
Swaptions
Compound Options

2. Interest Rate Caps (Caps)
Term (Tenor)
Reference Rate
Contract or Ceiling Rate or Strike price or Cap Rate
Notional Principal
Settlement Dates

3. Interest Rate Caps (Caps)
The writer of a cap pays the cap holder each time the contract’s reference rate is above the contract’s ceiling rate. It provides hedge against increase in interest rates.
Dealer Pays = D × Max [Reference – Ceiling, 0] × NP × LPP

4. Interest Rate Caps (Caps) Payoff Profile for a cap Purchaser (Per Settlement Period)
Profit
Max[Reference – Ceiling, 0] × NP
× LPP less Premium Paid
Ceiling Rate
Reference Rate
Per period premium (amortized)

5. Interest Rate Caps (Caps)
Per Period Cost (PPC)
= Total Premium ÷ PVIFAr/m, nm
Effective Annual Percentage Cost
= (1+PPC)m - 1

6. Interest Rate Caps (Caps)
A firm is in need of 4-year interest rate cap
on 6-month LIBOR. A dealer agrees to a
ceiling rate of 5% and the notional principal is
Rs.50 lakhs. The settlement dates are 1st Oct.
and 1st April every year and cap commences
on 1st April this year (2007). Given the value of
reference rate on different dates, the full set of
payments to the firm can be calculated.

7. Interest Rate Caps (Caps)
Payment Date Ref Rate Ceiling Rate LPP Payment
1st October /360 Rs.2,556
1st April /
1st October /
1st April /
1st October /360 Rs.1,277
1st April /360 Rs.2,514
1st October /360 Rs.3,067
1st April /
Rs.9,414

8. Interest Flows: Interest Rate Cap.
Cap
Dealer
Firm
LIBOR + 50bp
Lender
Max (LIBOR-5%,0)
4-yr rate cap
4-yr floating
rate borrowing

9. Rate Capped Swap: Interest Flows.
Swap
Dealer
Fixed rate
Firm
3rd party
lender
Fixed rate
Floating rate
Cap
Dealer
Cap on floating rate
Bank

10. Interest Rate Floors (Floors)
In case of an interest rate floor, the floor
writer pays the floor purchaser when the
reference rate drops below the contract rate
called the Floor Rate. The most common
usage is put a floor on the income from a
floating rate asset.

11. Interest Rate Floors Dealer Pays =
D × Max [Floor – Reference, 0] × NP × LPP

12. Payoff Profile for a Floor Purchaser (Per Settlement Period).
Profit
Max[Floor – Reference, 0] × NP × LPP
Less premium paid
Floor
Per period premium
(amortized)
Reference Rate

13. Interest Rate Floors A rate floor is not the mirror image of a rate
cap since the the cap and floor writers are not
the counter parties. The writer and purchaser
of a floor or of a cap are the counter parties.
This is due to the fact that option trading is a
zero-sum game.

14. Interest Rate Floors An insurance company which has 7.5% fixed
rate liability on the annuities it sold, invests in
floating rate 6-month treasury bills currently
yielding 7.75%. The management can invest
in fixed rate assets but will still be exposed to
the risk of interest rate predictions going
wrong.

15. Interest Rate Floors A floor is recommended wherein the company
should purchase a 10-year floor with a floor rate of
7.5% and the 6-month treasury-bill rate as the
reference rate. It pays up-front premium of 2.23%.
We can calculate its annual percentage cost at a
discount rate of 7.5% compounded semi-annually.
What are the implications if the rate on t-bills
remained below the floor rate and after five years
moved to 8.65%?

16. Interest Flows Floor Dealer, Firm & Annuity Holders.
T-Bills
6-month t-bill rate
Floor
Dealer
Max[7.5%-T Bill
Rate,0]
Annuity
Holders
Firm
7.5%
10-yr policy
10-yr rate floor

17. Interest Rate Collars (Collars)
It is a combination of a cap and a floor in
which the purchaser of a collar buys a cap and
simultaneously sells a floor. It can involve
two transactions of caps and floors or a single
transaction of a collar. It binds the purchaser
on both sides – locking into a band or
swapping into a band.

18. Payoff Profile for a Collar Purchaser (Per Settlement Period).
Profit
Cap settlement received
Less settlement paid and
net premium
Floor Rate
Ceiling Rate
Reference Rate
Difference between premium
paid on the cap and premium received
On the floor (per period equivalent)

19. How Interest Rate Collar Works?.
Assets
10%
Cap
Dealer
Floor
Max [prime-9.5%,0]
Lender
Firm
Prime Rate
Max [7%-prime, 0]

20. Working of a Collar Swap.
Swap
Dealer
Cap
Floor
dealer
Fixed Rate
Firm
Lender
LIBOR
Fixed rate
Max[LIBOR-Ceiling,0]
Max[floor-LIBOR,0]

21. A Participating Cap
It involves the purchaser of a cap to pay the dealer a portion of the difference between the reference rate and the ceiling rate when the reference rate is below the ceiling rate and the cap writer to pay the usual full difference between the reference rate and the ceiling rate when the reference rate is above the ceiling rate.

22. A Participating Cap Dealer Pays = D × [Max {RR – CR, 0} +
{ - PF × Max ( CR – RR, 0)}] NP × LPP
Here, CR is the Ceiling Rate, RR is the Reference Rate and PF is the Percentage Factor.

23. A Participating Cap
A firm needs a 5-year cap on a floating-rate liability tied to one-year LIBOR and wants to cap its rate at 9.75% on a notional principal of Rs.45ml. A cap dealer agrees to sell such a cap at an upfront premium of 2.60%. Firm feels that it is too high and agrees, under a participating cap, to pay 30% of the difference between RR and CR (9.75%) whenever RR falls below CR and the dealer will pay full difference between RR and CR whenever RR is above CR.

24. A Participating Cap
After 1 year on the first settlement day, 1-yr LIBOR stands at 9.24%, the dealer will pay
= × [Max {9.24% – 9.75%, 0} +
{ - 30% × Max (9.75% – 9.24%, 0)}]
Rs.45ml. × 365/360
= 0 + (-) Rs.69,806.25
i.e. the dealer receives from the firm Rs.69,806.25

25. The Caption
A registered service mark of Marine Midland Bank and introduced in mid 1980s, it is used as an option on option (cap) when a firm wants to lock-in the right to interest rate risk protection but is not sure that it will need protection. In the meantime the firm may look for better alternatives.

26. Why Caption?
A CFO wants to protect interest rate risk on floating rate financing by buying a 9% cap on an upfront premium of 2.16%, is not sure of the board approval but is apprehensive of cap rates going up. In the mean time he buys an option on this cap at a premium of 0.12%. If board approves, he exercises the option or else lets it expire. Even if the cap rates go down, he may let this option expire and buy another one.

27. The Swaption
It is an option on a swap wherein both parties agree to terms of the swap but the end user is not willing to commit to swap. After the life of this option expires, the end user could decide to either commit to swap terms or let the option expire. In case of not exercising, the premium is lost.

28. Monetizing the Embedded Options
Consider the following:
Is the return from investments in domestic and overseas affiliates making the firm vulnerable to interest rate and exchange rate movements?
Does the firm have exposure to commodity prices?
Is the debt paid in same currency as it is received?
Are there potential leverage concerns?

29. Monetizing the Embedded Options
If a firm holds embedded options (which can be found out by digging the financial statements), it can write offsetting options and this can be viewed as writing covered options. It transforms future value into present value.

30. A Risky Bond as a Compound Option.
Bond matures
pay
Don’t pay
option
default
pay
Compound
option
Don’t pay
default
pay
Compound
option
Don’t pay
default
pay
Don’t pay
Compound
option
default