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 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 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.

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 LIBOR + 50bp Lender Max (LIBOR-5%,0) 4-yr rate cap 4-yr floating rate borrowing

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

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) . Profit Max[Floor – Reference, 0] × NP × LPP Less premium paid Floor Per period premium (amortized) Reference Rate

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 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%?

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

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 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)

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

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]

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 . 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