Multi-period Options

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 contracts reference rate is above the
  contracts 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

MaxReference Ceiling, 0 NP LPP less
Premium Paid
Ceiling Rate
0
Reference Rate
Per period premium (amortized)
5
Interest Rate Caps (Caps)

• Per Period Cost (PPC)
• Total Premium PVIFAr/m, nm
• Effective Annual Percentage Cost
• (1PPC)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 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

8
Interest Flows Interest Rate Cap

• .

Cap Dealer
Firm
Lender
LIBOR 50bp
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
MaxFloor Reference, 0 NP LPP Less
premium paid
Floor
Per period premium (amortized)
0
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 FlowsFloor Dealer, Firm Annuity
Holders

• .

T-Bills
6-month t-bill rate
Floor Dealer
Annuity Holders
Max7.5-T Bill Rate,0
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
0
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 Dealer
Lender
Max prime-9.5,0
Firm
Prime Rate
Max 7-prime, 0
20
Working of a Collar Swap

• .

Swap Dealer Cap Dealer Floor dealer
Fixed Rate
Firm
Lender
LIBOR
Fixed rate
MaxLIBOR-Ceiling,0
Maxfloor-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
• 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

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
Dont pay
option
default
pay
Compound option
Dont pay
default
pay
Dont pay
Compound option
default
pay
Dont pay
Compound option
default