Transcript Com 4FJ3 - McMaster University

Com 4FJ3
Fixed Income Analysis
Week 11
Options, Swaps, & Credit Derivatives
Option Basics
• Options are based on buying or selling an
asset in the future at a fixed price
• This transaction is not guaranteed to take
place
• With an option one party to the option
decides whether or not the transaction will
be completed on the specified date
2
Option Basics
• The option has given one party the right but
not an obligation to buy or sell the asset at
the fixed price
• As you might guess, this party has to pay
the other party for this privilege
• The payment is called the option premium
3
Options on Physical
• Few options on physical are still traded in
the fixed income segment, US treasury is
most active on CBOE
– mainly replaced by futures options
• Some OTC markets remain
• Institutional investors hedging specific
securities are the most common, so the lack
of liquidity is not a problem
4
Option Terminology
•
•
•
•
•
•
Call option: the right to buy an asset
Put option: the right to sell an asset
Exercise: deciding to buy or sell the asset
Exercise price: the predetermined price
Strike price: the predetermined price
Expiration date: the last day that the option
can be exercised
5
Option Terminology
• American option: can be exercised at any
time on or before the expiration date
• European option: can only be exercised on
the expiration date
– Note: although most options are American,
most pricing models assume European options
– This assumption is acceptable if the option is
not on a dividend paying share or similar asset
6
Option Jargon
• In the money: an option that would yield a
profit if exercised today
• Out of the money: an option that can not be
profitably exercised at the current market
prices
• At the money: an option where the exercise
price is the same as the current market price
7
Basic Option Positions
• Buy a call option
– Pay a premium to buy at specified price
• Write a call option
– Sell the right to buy from you
• Buy a put option
– Pay a premium to sell at specified price
• Write a put option
– Sell the right to sell to you
8
Option Payoffs
• For the buyer, if the price
moves in their favour, they
will gain on exercise
• If the price moves in the
other direction, they will
allow the option to expire
unused, so the payoff will
be zero
Call Option Payoff Profile
Payoff
Exercise Price
Market
Price
9
Payoff Example
• Given the following
options, expiring
today, find the payoff
Option
A
B
C
D
Type
Call
Call
Put
Put
Strike
Price
$25
$30
$20
$15
Market
Price
$24
$37
$18
$18
• Option A allows the
owner to purchase the
asset for $25
• Without the option she
can purchase that asset
for $24
• The option should not
be exercised so its
payoff is zero
10
Payoff Example
• Given the following
options, expiring
today, find the payoff
Option
A
B
C
D
Type
Call
Call
Put
Put
Strike
Price
$25
$30
$20
$15
Market
Price
$24
$37
$18
$18
• With option B the investor
can buy the asset for $30 and
immediately sell it for $37
– This is a payoff of $7
• Option C allows the investor
to sell the asset for $20, she
can replace it for $18
– Payoff = $2
• Option D is worthless
– Payoff = $0
11
Option Profits
• For the option holder profit equals the
payoff minus the price paid for the option
• For the writer the profit equals the premium
received minus the payoff that the holder
gets at exercise, if any
• Breakeven is the market price where the
payoff equals the initial premium
12
Option Value
• Intrinsic value: how much of a profit you
could make if you exercised the option
today
– Minimum of 0 since exercise is not mandatory
• Time value: the difference between the
current price of an option and its intrinsic
value
13
Logical Limits
• What is the maximum price at which a call
option should trade?
– Since it gives you the right to buy the asset at a
fixed price the maximum price of a call option
should be the current price of the asset
• What is the minimum price?
– The option should sell for at least its intrinsic
value, below that price it is better to exercise
the option than to sell the option
14
Call Option Price
Value
option price
intrinsic value
Exercise Price
Market
Price
15
Time Value
• An option which can be profitably exercised
today will have a positive intrinsic value
• Should you exercise that option?
– In most cases the answer is no
– The reason is that the intrinsic value is the
minimum price of the option and the option is
likely selling for more than the minimum
16
Time Value
• The difference, between the intrinsic value
and price is the time value of the option
• As the time to expiry approaches zero, the
time value of the option approaches zero
• Exercising an option before expiry yields
only the intrinsic value, the time value of
the option is lost
17
When to Exercise Early
• The main reason to consider exercising an
option early is if the option is on an asset
that has periodic cash flows
• If the option is on a bond that will pay a
coupon tomorrow, and the coupon is larger
than the remaining time value of the option,
it would make sense to exercise the option
to get that coupon
18
Futures Options
• The right to enter into a futures contract at a
pre-specified price
• Call option: the right to take a long position
• Put option: the right to take a short position
• If exercised, the futures contract is written
at the specified price, and immediately
marked to market by the exchange
19
Exercise Example
• Call option on futures contract at $85
• Current futures price $90
• On exercise; writer agrees to sell for $85,
call owner agrees to buy for $85
• Immediately marked to market
– writer pays the exchange $5
– call owner gets $5 from the exchange
20
Margin Requirements
• Buyer of option faces no chance of losing
money beyond what was paid for the option
so they post no margin
• Writer of option must post a margin equal
to the margin requirement of the underlying
contract plus the option premium
• Writer can be subject to margin calls
21
Why Futures Options
• No Accrued interest payments
• No concern about a delivery squeeze
– you don’t need to deliver a physical asset
– there is no cost to enter a futures contract
• Pricing of the option requires knowing the
value of the underlying asset at all times,
easy with futures contracts
22
Traded Futures Options
• Active market for all futures contracts listed
in the previous lecture
– T-bond and T-note on CBOT
– Eurodollar CD on IMM
• All contracts are American
• CBOT competing with OTC by introducing
the flexible treasury futures options
23
Option Pricing
• Six factors affect the price of an option
–
–
–
–
–
–
Current price on underlying (S)
Strike or exercise price (X)
Time to expiry (t)
Risk free rate (Rf)
Expected price volatility (s)
Coupon rate on bond; higher coupon rates will
make owning the bond better than the option
24
Black-Scholes
• Most popular option pricing model
C  SN d1   XN d 2 e
Rf t
N(d1) means the area under
the cumulative standard
normal distribution curve
with respect to d1.
1 
S 
ln    R f  s 2   t
X
2 
d1    
s t
1 
S 
ln    R f  s 2   t
X
2 
d2    
 d1  s t
s t
25
Put Option Pricing
• How much is a put option worth?
• If we buy an asset and a put option on that
asset and we sell a call option that has the
same strike price (both European), how
much will this portfolio be worth at the end
of the time period?
26
Put-Call Parity
• Whether the market value is above or below
the strike price, the value of the portfolio
will be the strike price of the options.
– S + P - C = X /(1 + Rf)
– P = X /(1 + Rf) + C - S
• This is known as Put-Call Parity.
27
Problems with Bond Options
• The maximum value of a bond is the
undiscounted future cash flows
• Black-Scholes can give a positive value to a
call option with a strike price greater than
the undiscounted future cash flows
• Price volatility varies with time, interest rate
volatility is more appropriate as an input
28
Arbitrage-Free Binomial Model
• A popular model with dealer firms is the
Black-Derman-Toy model
• Uses the interest rate ladder method shown
in lecture 9
• Also assumes European options
• Only the volatility component is not
observable
29
Valuing Futures Options
• Most popular model is Fischer Black
• Similar concerns to Black-Scholes
R t
C  FN d1   XN d 2 e
R t
P  XN  d 2   FN  d1 e
f
f
F 1 2
ln   s t
X
2
d1   
s t
d 2  d1  s t
30
Option Strategy
• Most common hedge strategy is the
protective put to guard against a large
decrease in value
• Covered call strategy attempts to enhance
yield, but limits price appreciation
• Which is best depends on the goals of the
portfolio management
31
Interest Rate Swaps
• Main idea is to trade fixed rate interest
payments (receipts) for floating rate
payments (receipts)
• Swaps have counterparty risks since they
are not traded on organized exchanges
• May involve a securities firm or
commercial bank as a broker or dealer
32
Swap Example
• Company Z has a bond issue outstanding
with a face $50 m and a coupon of 9%
• The firm would prefer a floating rate
• The firm enters into a swap arrangement to
pay LIBOR on $50 m, and in return
receives $2.25 every six months in return
• Typically only the difference is paid
33
Interpreting a Swap
• There are 2 ways of looking at a swap
• A package of forward contracts
• A package of cash market instruments
– Buy a 9% fixed coupon $50m bond
– Finance by borrowing $50 at LIBOR
34
Valuing a Swap
• At inception, the swap contract will have a
value of zero, the present value of the traded
cash flows should be the same or one of the
parties will not enter the contract
• As interest rates change, the swap can
increase or decrease in value
35
Beyond Plain Vanilla
• Varying principal swaps: the principal on
which interest is calculated changes over
time… often for amortizing securities
• Basis swaps: exchanging floating rate
payments based on different reference rates
– Constant Maturity Swap: one of the reference
rates is the constant maturity treasury (CMT)
rate published by the federal reserve
36
Beyond Plain Vanilla
• Swaptions: an option to enter into a swap
contract at a point in the future
• Forward start swap: a swap contract were
the start date of the swap is in the future
37
Interest Rate Agreements
• Similar to a series of interest rate options or
insurance policies
• For an upfront payment, one party agrees to
pay compensation for unfavourable interest
rate movements, paid periodically over the
life of the agreement
• Also called caps or floors
38
Caps and Floors
• Interest rate agreements include
–
–
–
–
–
The reference rate
The strike rate (cap or floor)
The length of the agreement
The frequency of settlement
The notional principal
39
Cap Example
• A 9% cap is sold on LIBOR for a 5 year
period with semi-annual settlement on a
notional principal of $5 m
• If in the next period LIBOR is 8.75%, there
is no payment since it is under the cap
• If LIBOR is 9.25% half a year later, there is
a payment of $6,250
• (0.0925-0.09)/2 x 5,000,000
40
Valuing Caps and Floors
• Done using the binomial interest rate lattice
method in chapter 24
• The value of each individual possible
payment date (caplet or floorlet) is found
independently and summed
• The value at any node is either zero if the
cap/floor has not been violated, or the
amount of payment that is required
41
Collars
• The simultaneous buying of a cap and
selling a floor
• Often offered to the floating rate payer by a
swap dealer, the effect is to restrict the
floating rate to a certain range
42
Credit Derivatives
• Similar to the way interest rate derivatives
allow the transfer of some of the interest
rate risk, credit derivatives allow an investor
to transfer credit risk to others
• These derivatives are often more efficient to
use than actual cash market postions
43
Types of Credit Risk
• Default risk
– the issuer of the security fails to make the
promised payments
• Credit spread risk
– due to a credit upgrade or downgrade, the
required yield spread over treasury changes,
affecting the price of the bond
44
ISDA
• International Swap and Derivatives
Association
• Since 1998 has set standard contracts for
credit default swaps and total return swaps
• The contracts are flexible enough to use for
the other derivatives listed
45
References
• The contracts are based on some underlying
security, referred to as:
– reference entity or reference issuer; the firm
that issued the bond and who’s credit risk is
being transferred
– reference obligation or reference asset; the
particular bond issue (or other debt instrument)
that is being protected
46
Credit Events
• Many of the derivatives pay off when a
particular event happens
– Bankruptcy
– Failure to pay
– Obligation acceleration; the firm violates a term
in the covenant making the bond due & payable
– Repudiation/moratorium; rejecting the above
– Restructuring; controversial, see next slide
47
Restructuring
• Prior to seeking bankruptcy protection, a
debtor can make a proposal to creditors or
seek a restructuring of their debt
• Problematic due to the discretion of the
holders of the debt to accept the proposal
• IDSA form has 4 different methods of
handling restructuring in the contract
– none, all, modified and modified modified
48
Asset Swap
• Not strictly a credit derivative since credit
risk is not traded
– Own a bond paying fixed coupons, enter a swap
agreement to trade fixed for floating payments
– Sell the asset to a dealer with a swap agreement
and an obligation to buy back the bond if there
is a credit event
49
Total Return Swap
• A swap agreement where one party makes
floating rate payments and the counter party
makes payments based on the total return
(interest and capital gain/loss) of the
reference obligation
• Cash flow of the total return payer is similar
to short selling the reference obligation and
investing the proceeds
50
Credit Default Swap
• Buyer pays a premium (a % of the notional
amount), on a quarterly basis, to protect
against default
• In the event of a credit event, the seller of
the swap buys the underlying asset from the
buyer for the notional amount
• Can be based on a basket of assets
51
Credit Spread Options
• Underlying is a reference obligation
– a call or put option where the strike price is not
fixed but based on a fixed spread over treasury
• Underlying is the credit spread
– a cash settlement contract where the payoff is
based on the difference between the reference
obligation’s credit spread vs. the strike spread
x notional amount x risk factor
52
Credit Spread Forwards
• Similar to the difference between forward
contracts and option contracts on any other
commodity
• Related to a credit spread option, but the
final settlement is not based on one party
having the choice to exercise, so no option
premium is required
53
Structured Credit Products
• Debt instruments with payoffs linked to the
credit performance of reference obligations
• Synthetic CDO: Invests in low risk assets
and sells credit protection derivatives
– Dominates the CDO market
• Credit-linked notes: short term debt, 1 - 3
years; if the reference asset defaults the note
is paid off early and at a discount
54