Multi-period Options

• Interest Rate Caps

• Interest Rate Floors

• Interest Rate Collars

• Captions

• Swaptions

• Compound Options

Interest Rate Caps (Caps)

• Term (Tenor)

• Reference Rate

• Contract or Ceiling Rate or Strike price or Cap Rate

• Notional Principal

• Settlement Dates

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

Interest Rate Caps (Caps)Payoff Profile for a cap Purchaser (Per Settlement Period)

Profit

0

Max[Reference – Ceiling, 0] × NP × LPP less Premium Paid

Ceiling Rate

Reference Rate

Per period premium (amortized)

Interest Rate Caps (Caps)

Per Period Cost (PPC)

= Total Premium ÷ PVIFAr/m, nm

Effective Annual Percentage Cost

= (1+PPC)m - 1

Interest Rate Caps (Caps)

A firm is in need of 4-year interest rate cap on 6-month LIBOR. A dealer agrees to aceiling rate of 5% and the notional principal isRs.50 lakhs. The settlement dates are 1st Oct.and 1st April every year and cap commenceson 1st April this year (2007). Given the value ofreference rate on different dates, the full set ofpayments to the firm can be calculated.

Interest Rate Caps (Caps)

Payment Date Ref Rate Ceiling Rate LPP Payment

1st October 07 5.10 5.00 184/360 Rs.2,556

1st April 08 4.92 5.00 182/360 0

1st October 08 4.95 5.00 184/360 0

1st April 09 4.90 5.00 181/360 0

1st October 09 5.05 5.00 184/360 Rs.1,277

1st April 10 5.10 5.00 181/360 Rs.2,514

1st October 10 5.12 5.00 184/360 Rs.3,067

1st April 11 4.89 5.00 181/360 0

Rs.9,414

Interest Flows: Interest Rate Cap.

Cap Dealer

Firm LenderMax (LIBOR-5%,0)

4-yr rate cap

LIBOR + 50bp

4-yr floating rate borrowing

Rate Capped Swap: Interest Flows

.

Swap Dealer

Cap Dealer

Firm3rd partylender

Bank

Fixed rate

Floating rate

Cap on floating rate

Fixed rate

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.

Interest Rate Floors

Dealer Pays =

D × Max [Floor – Reference, 0] × NP × LPP

Payoff Profile for a Floor Purchaser (Per Settlement Period)

.

Reference Rate

Profit

0

Max[Floor – Reference, 0] × NP × LPP Less premium paid

FloorPer period premium(amortized)

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.

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.

Interest Rate Floors

A floor is recommended wherein the companyshould purchase a 10-year floor with a floor rate of7.5% and the 6-month treasury-bill rate as thereference rate. It pays up-front premium of 2.23%.We can calculate its annual percentage cost at adiscount rate of 7.5% compounded semi-annually.What are the implications if the rate on t-billsremained below the floor rate and after five yearsmoved to 8.65%?

Interest FlowsFloor Dealer, Firm & Annuity Holders

.

FloorDealer

Firm

T-Bills

AnnuityHolders10-yr rate floor

Max[7.5%-T BillRate,0]

6-month t-bill rate

7.5%

10-yr policy

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.

Payoff Profile for a Collar Purchaser (Per Settlement Period)

.

Profit

0Reference Rate

Floor Rate Ceiling Rate

Difference between premium paid on the cap and premium receivedOn the floor (per period equivalent)

Cap settlement receivedLess settlement paid and net premium

How Interest Rate Collar Works?.

CapDealer

FloorDealer

Firm

Assets

Lender

10%

Prime RateMax [prime-9.5%,0]

Max [7%-prime, 0]

Working of a Collar Swap.

Swap Dealer

Cap Dealer

Floordealer

Firm Lender

Fixed Rate

LIBOR

Max[LIBOR-Ceiling,0]

Max[floor-LIBOR,0]

Fixed rate

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.

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.

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.

A Participating Cap

After 1 year on the first settlement day, 1-yr LIBOR stands at 9.24%, the dealer will pay

= +1 × [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

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.

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.

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.

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?

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.

A Risky Bond as a Compound Option.

default

default

default

default

Don’t pay

Don’t pay

Don’t pay

Don’t pay

Compoundoption

pay

Compound option

pay

Compound option

pay

option

pay

Bond matures