2.3.1 Bull Spreads A.Bull Call Spread: This strategy involves a combination of a long position in a call with a lower exercise price and a short position in a call with a higher exercise
Trang 1Reading 29 Risk Management Applications of Option Strategies
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2.2 Risk Management Strategies with Options and the Underlying
An investor can reduce exposure without selling the
underlying by:
1)Selling a call on the underlying i.e covered call
2)Buying a put i.e protective put
2.2.1) Covered Calls Covered Call = Long stock position + Short call position
Covered Call is appropriate to use when an investor:
• Expects that stock price will neither increase nor
decrease in near future
Characteristics:
• It is an imperfect form of portfolio protection It
provides only limited downside protection
• It exchanges “upside” potential for current income
in the form of option premium
• It generates cash up front in the form of option
premium but removes some of the upside
potential
• It reduces both the overall risk and the expected
return compared with simply holding the
underlying This loss in potential upside gains is
compensated by option premium received by
selling a call
• Writers of covered call options make small
amounts of money, but make it often; because
expected profits come from rare but large
pay-offs
To summarize:
a)Value at expiration = Value of the underlying +
Value of the short call = VT = ST – max (0, ST – X)
b)Profit = Profit from buying the underlying + Profit
from selling the call = VT – S0 + c0
c)Maximum Profit = X – S0 + c0
d)Max loss would occur when ST = 0 Thus, Maximum
Loss = S0 – c0
e)Breakeven =ST* = S0 – c0
It is important to note that options do not always automatically increase risk
• Selling a call option on a stock already owned by
an investor reduces the overall risk
• Selling a call without owning the stock exposes the investor to unlimited loss potential
Thus, covered call should not be viewed as a conservative strategy
Relationship between exercise price and potential upside gains for the short call:
• The higher the exercise price of the call option, the lower the price of an option and thus short call receives lower premium However, in this case, short call has a greater opportunity to gain from the upside
NOTE:
Current value of the asset should be viewed as an opportunity cost of an investor
2.2.2) Protective Puts Protective Put = Long stock position + Long Put position This provides protection against a decline in value
It is similar to “insurance" i.e buying insurance in the form
of the put, paying a premium to the seller of the insurance, the put writer
Characteristics:
• It provides downside protection while retaining the upside potential
• It requires the payment of cash up front in the form
of option premium
• The higher the exercise price of a put option, the more expensive the put will be and consequently the more expensive will be the downside
protection
Protective put is appropriate to use when:
• An investor owns a stock and does not want to sell
it
• An investor expects a decline in the value of the stock in the near future but wants to preserve upside potential
To summarize:
a)Value at expiration: VT = ST + max (0, X - ST)
Practice: Example 3, Volume 5, Reading 29
Trang 2b)Profit = VT – S0 - p0
c)Maximum Profit = ∞
asset is sold at exercise price Thus,
Maximum Loss = S0 + p0 – X
e)In order to breakeven, the underlying must be at
least as high as the amount paid up front to
establish the position Thus, Breakeven =ST* = S0 +
p0
Example:
Strike price = X = $45
Option cost = p0 = $6
• The maximum possible loss is $6
• The potential gain is unlimited
Put v/s Insurance:
The exercise price of the put is like the insurance
deductible because the magnitude of the exercise
price reflects the risk assumed by the party who owns
the underlying A higher exercise price of the put option
is equivalent to a lower insurance deductible
• The higher the exercise price, the higher the option
premium and the less risk assumed by the holder of
the underlying and the more risk assumed by the
put seller
• In insurance, the higher the deductible, the more
risk assumed by the insured party and the less risk
assumed by the insurer
A spread is a strategy that involves buying one option
and selling another identical option but either with
different exercise price or different time to expiration
Time Spread: When the options have different time to
expiration, the spread is called a time spread Time
spread strategies are used to exploit differences in
perceptions of volatility of the underlying e.g an investor
buys an option with a given expiration and exercise
price and sells an option with the same exercise price
but a different time to expiration Time spread can benefit from high volatility
Money spreads: When the options have different
exercise price, the spread is called a money spread e.g
an investor buys an option with a given expiration and exercise price and sells an option with the same expiration but a different exercise price
• Note that the options are on the same underlying
asset
2.3.1) Bull Spreads
A.Bull Call Spread: This strategy involves a combination
of a long position in a call with a lower exercise price and a short position in a call with a higher exercise price i.e
• Buy a call (X1) with option cost c1 and sell a call (X2) with option cost c2, where X1< X2 and c1 > c2
Note that the lower the exercise price of a call option,
the more expensive it is
Rationale to use Bull Call Spread: Bull call spread is used
when investor expects that the stock price or underlying asset price will increase in the near future
Characteristics:
• This strategy gains when stock price rises/ market goes up
• Like covered call, it provides protection against downside risk but provides limited gain i.e upside potential
• It is similar to Covered call strategy i.e
o In covered call, short position in call is covered
by long position in underlying
o In bull call spread, the short position in the call with a higher exercise price is covered by long position in the call with a lower exercise price
To summarize:
a)The initial value of the Bull call spread = V0 = c1 –
c2 b)Value at expiration: VT = value of long call – Value
of short call = max (0, ST – X1) - max (0, ST – X2) c)Profit = Profit from long call + profit from short call Thus,
Profit = VT – c1 + c2 d)Maximum Profit = X2 – X1 – c1 + c2 e)Maximum Loss = c1 – c2
f) Breakeven =ST* = X1 + c1 – c2
Practice: Example 4,
Volume 5, Reading 29
Trang 3B.Bull Put spread: In bull put spread, investor buys a put
with a lower exercise price and sells an otherwise
identical put with a higher strike price
• Buy a put (X1) and sell a put (X2), with X1< X2
• Since put with a higher exercise price (X2) is
expensive than a put with a lower exercise price
(X1), bull put spread generates cash inflow at
initiation of the position
• Profit occurs when both put options expire
out-of-the-money i.e investor will earn net premium
• It is identical to the sale of Bear put spread
• Bull put spread pay-off diagram is the mirror-image
of the pay-off diagram of bear put spread
2.3.2) Bear Spreads
A.Bear Put Spread: This strategy involves a combination
of a long position in a put with a higher exercise price
and a short position in a put with a lower exercise
price i.e
• Buy a put (X2) with option cost p2 and sell a put (X1)
with option cost p1, where X1 < X 2 and p 1 < p 2
Note that the higher the exercise price of a put option,
the more expensive it is
Rationale to use Bear Put Spread: Bear Put spread is used
when investor expects that the stock price or underlying
asset price will decrease in the future
To summarize:
a)The initial value of the bear put spread = V0 = p2 –
p1
b)Value at expiration: VT = value of long put – Value
of short put = max (0, X2 - ST) - max (0, X1 - ST)
c)Profit = Profit from long put + profit from short put
Thus,
Profit = VT – p2 + p1
d)Maximum Profit occurs when both puts expire
in-the-money i.e when underlying price ≤ short put
exercise price (ST ≤ X1),
• Short put is exercised and investor will buy an
asset at X1 and
• This asset is sold at X2 when long put is exercised
Thus,
Maximum Profit = X2 – X1 – p2 + p1
out-of-the-money and investor loses net premium i.e when ST> X2 Thus,
Maximum Loss = p2 – p1 f) Breakeven =ST* = X2 – p2 + p1
B Bear Call Spread: In bear call spread, investor sells a call with a lower exercise price and buys an otherwise identical call with a higher strike price
• Sell a call (X1) and buy a call (X2), with X1< X2.
• Since call with a lower exercise price (X1) is expensive than a call with a higher exercise price (X2), bear call spread generates cash inflow at initiation of the position
• Profit occurs when both call options expire out-of-the-money i.e investor will earn net premium
• It is identical to the sale of a bull call spread i.e it is used when investor expects a decline in stock price
• Bear call spread pay-off diagram is the mirror-image of the pay-off diagram of bull call spread
2.3.3) Butterfly Spreads
Butterfly spread strategy is a combination of a bull and
bear spread Butterfly spreads perform based on the volatility of the underlying
A.Long Butterfly Spread (Using Call):
Long Butterfly Spread = Long Bull call spread + Short Bull call spread (or Long Bear call spread)
Long Butterfly Spread = (Buy the call with exercise price
of X1 and sell the call with exercise price of X2) + (Buy the call with exercise price of X3 and sell the call with
exercise price of X2)
where,
X1< X2 < X3 Cost of X1 (c1) > Cost of X2 (c2) > Cost of X3 (c3) NOTE:
Long Butterfly spread requires cash outlay at initiation because bull spread purchased by an investor is expensive than a bull spread that is sold
Practice: Example 6, Volume 5, Reading 29
Practice: Example 5,
Volume 5, Reading 29
Trang 4Rationale to use Long Butterfly Spread: It is used when
investor expects that the volatility of the underlying will
be relatively low compared to what market expects i.e
the underlying asset will trade near the middle exercise
price
• When market is highly volatile, butterfly spread
strategy is not profitable and generates losses
To summarize:
a)Value at expiration: VT = max (0, ST – X1) – 2 max
(0, ST – X2) + max (0, ST – X3)
b)Profit = VT – c1 + 2c2 - c3
c)Maximum Profit occurs when price of underlying is
close to the middle exercise price i.e when ST =
X2 Thus,
Maximum Profit = X2 – X1 – c1 + 2c2 – c3
d)Maximum Loss occurs when price of underlying <
lower strike price or > upper strike price and
investor loses net premium Thus, Maximum Loss =
c1 – 2c2 + c3
e)There are two breakeven points i.e
i Breakeven =ST* = X1 + net premium = X1 + c1 –
2c2 + c3
ii Breakeven = ST* = 2X2 – X1 – Net premium = 2X2
– X1 – (c1 – 2c2 + c3 ) = 2X2 – X1 – c1 + 2c2 - c3
NOTE:
• Purple line represents after 1 month
• Light Green line represents after 3 months
• Dark Green line represents at expiry
B.Short Butterfly Spread(Using Call): It refers to selling the
butterfly spread i.e
Short butterfly spread = Selling the calls with exercise
prices of X1 and X3 and buying two calls with exercise
prices of X2
Rationale to use Short butterfly Spread: This strategy is
preferably used when investor expects that the volatility
of the underlying will be relatively high compared to
what market expects
• The maximum profit occurs when either all four of
the options are out-of-the money or all four are
in-the-money i.e investor earns net premium
Maximum Profit = c1 + c3 – 2c2
C.Long Butterfly Spread (Using Puts):
Butterfly Spread = Long Bear put spread + Short bear put spread (or Long Bull put spread)
Long Butterfly Spread = (Buy the put with exercise price
of X3 and sell the put with exercise price of X2) + (Buy the put with exercise price of X1 and sell the put with
exercise price of X2)
where,
X1< X2 < X3 Cost of X1 (p1) < Cost of X2 (p2) <Cost of X3 (p3)
D.Short Butterfly Spread (Using Puts): It refers to selling the butterfly spread i.e
Short butterfly spread = Selling the puts with exercise prices of X1 and X3 and buying two puts with exercise prices of X2
• The maximum profit occurs when either all four of the options are out-of-the money or all four are in-the-money i.e investor earns net premium
Maximum Profit = p3 + p1 – 2p2 NOTE:
When options are priced correctly, butterfly spread using calls will provide the same result as butterfly using puts
2.4.1) Collars Collar refer to the strategy in which the cost of buying put option can be reduced by selling a call option
• When call option premium is equal to put option premium, no net premium is required up front This strategy is known as a Zero-Cost Collar *
• This strategy provides downside protection at the expense of giving up upside potential Therefore, zero-cost only refers to the fact the no cash is required to be paid up front
Practice: Example 7, Volume 5, Reading 29
Trang 5• In Zero-cost collar, first of all investor selects
exercise price of the put option Then, the call
exercise price is set such that the call premium
offsets the put premium so that there is no initial
outlay for the options
• Typically,
o Put exercise price (e.g X1) < current value of the
underlying
o Call exercise price (e.g X2) must be > current
value of the underlying
• When price < X1, put provides protection against
loss
• When price > X2, short call reduces gains
• When price lies between X1 and X2, both put and
call are out-of-the-money
*NOTE:
Typically, in a collar, the call and put premiums offset
each other However, it is not necessarily always the
case i.e call premium can be > put premium
Important to note:
• Put premium decreases when put exercise price is
lowered
• To offset this lower put premium, investor can sell
call option with a higher exercise price
• Decreasing put exercise price and increasing call
exercise price results in increase in both the upside
potential and downside risk
Collar v/s Bull Spread: The collar is quite similar to a bull
spread i.e both have a cap on the gain and a floor on
the loss However, bull spread does not involve actually
holding the underlying
To summarize:
(For zero-cost collar)
a)Initial value of the position = value of the
underlying asset = V0 = S0
b)Value at expiration: VT = Value of underlying ST +
Value of the put option + Value of the short call
option = ST + max (0, X1 - ST) – max (0, ST – X2)
c)Profit = VT – V0 = VT –S0
d)Maximum Profit = X2 – S0
e)Maximum Loss = S0 – X1
f) Breakeven =ST* = S0
Range forwards and risk reversals: Collars are also known
as range forwards and risk reversals
• Like forwards, collar requires no initial outlay except the underlying price
• Unlike forwards, collar payoff represents a range as
it is shown in the figure above that it breaks at the two exercise prices
• Collars represent directional strategies i.e their performance is based on the direction of the movement in the underlying
2.4.2) Straddle
A Long straddle: It involves buying a put and a call with same strike price on the same underlying with the same expiration; both options are at-the-money
• In this strategy, an investor can make profit from upside or downside movement of the underlying price
• Due to call option, the gain on upside is unlimited and due to put option, downside gain is quite large but limited
• Straddle is a strategy that is based on the volatility
of the underlying It benefits from high volatility
• Straddle is a costly strategy
Rationale to use Straddle: Straddle is to be used only when the investor expects that volatility of the underlying will be relatively higher than what market expects but is not certain regarding the direction of the movement of the underlying price
To summarize:
a)Value at expiration: VT = max (0, ST -X) + max (0, X–
ST) b)Profit = VT –p0 - c0 c)Maximum Profit = ∞
options expire at-the money and investor loses premiums on both options i.e
Maximum Loss = p0 + c0 e)Breakeven = ST* = X ± (p0 + c0)
B Short Straddle: It involves selling a put and a call with same strike price on the same underlying with the same expiration; both options are at-the-money
Practice: Example 8, Volume 5, Reading 29
Trang 6• This strategy is preferably used when investor has
neutral view of the volatility or when investor
expects a decrease in volatility
• This strategy gains when both the options expire
at-the money i.e investor earns call and put
premium
• This strategy has unlimited loss potential
Variations of Straddle: When investor has any specific
outlook regarding direction of price movement, then
either a call or a put can be added to the straddle
• Adding call option to a straddle is known as
“Strap”
• Adding put option to a straddle is known as “Strip”
• These strategies generate greater gains when
price movement occurs in the expected direction;
however, these strategies are more complex than
a straddle
a)Long Strangle: It is a variation of the straddle This
strategy involves buying the put and call on the same
underlying with the same expiration but with different
exercise prices This strategy is used if investor view is
that volatility will increase
b)Short Strangle: This strategy involves selling the put
and call on the same underlying with the same
expiration but with different exercise prices This
strategy is used if investor has a neutral view about
volatility or he/she expects that volatility will decrease
2.4.3) Box Spreads
A box spread is a combination of a bull spread and a bear spread i.e
Box-spread = Bull spread + Bear spread
A.Long Box-spread= (buy the call with exercise price X1 and sell the call with exercise price X2) + (buy the put with exercise X2 and sell the put with exercise X1)
• Box spread pay-off (i.e profit) is always the same i.e it is must be risk-free when the options are priced correctly * In simple words, box-spread always results in buying the underlying at X1 and selling it at X2 Since this outcome is known to an investor at the start, a box-spread can be viewed
as a riskless strategy
• Since transaction is risk free, the PV of the pay-off, discounted at risk-free rate should be equal to the initial outlay (net premium) i.e we should have: (X2 – X1) / (1 + r) r = c1 – c2 + p2 – p1
o When PV of the pay-off > net premium, the box spread is underpriced and it should be
purchased Buying a box-spread is referred to as long box-spread
o When PV of the pay-off < net premium, the box spread is overpriced and it should be sold It is referred to as short box-spread
*Arbitrage opportunity is available when options are not priced correctly
B Short Box-spread = (Sell the call with exercise price X1 and buy the call with exercise price X2) + (Sell the put with exercise X2 and buy the put with exercise X1)
Advantages:
• A box spread can be used to exploit an arbitrage opportunity
• A box spread does not require the binomial or Black-Scholes-Merton model to hold
• It does not require a volatility estimate and all the transactions associated with box-spread strategy can be executed within the options market
• Box-spread is a simple strategy and has lower transaction costs
Practice: Example 9, Volume 5, Reading 29
Trang 7To summarize (for Long Box-spread):
a)Initial value of the box spread = Net premium = c1
– c2 + p2 – p1
b)Value at expiration: VT = X2 –X1
c)Profit = X2 –X1 - (c1 – c2 + p2 – p1)
d)Maximum Profit = same as profit
e)Maximum Loss = no loss is possible given fair
option prices
f) Breakeven =ST* = no break-even; the transaction
always earns the risk-free rate, given fair option
prices
Volatility will increase
Neutral view
on volatility
Volatility will decrease
Price will decrease
Underlying
Sell Calls
Neutral view on price
Buy Straddle
Price will increase
Underlying
Sell Puts
Interest rate call and put options are used to protect
against changes in interest rates
• For dollar based interest rate options, generally,
the underlying rate is LIBOR
• The underlying rate is always a specific rate i.e the
rate on 90-day or 180-day underlying instrument
• When the option is exercised, the pay-off is
determined using a specific notional principal
• Traditionally, the pay-off on interest rate option
does not occur immediately upon exercise; rather,
it is paid on the date when payment on the
underlying instrument is due
The pay-off of an interest rate Call Option= (Notional
principal) × max (0, Underlying rate at expiration –
• 180-day LIBOR can be used as the underlying rate
and days in underlying could be 180 or perhaps
182, 183 etc
• When an interest rate option is based on m-day
LIBOR, it is important to note that the rate is
determined on the day when the option expires
and payment is made m days later
The pay-off of an interest rate Put Option= (Notional
principal) × max (0, Exercise rate - Underlying rate at
Interest rate call options are used by borrowers to manage interest rate risk on floating-rate loans In interest rate call options, the following factors must be considered
1)Option expiration date is the same as when loan starts
2)Option pay-offs occur at the time when borrower makes interest payments on loan
(i.e at time t0)
Example:
A company plans to borrow $40 million in 128 days at 180-day LIBOR plus 200 basis points To manage the risk associated with higher interest rate on a loan, it buys a call option in which the underlying is the rate on 180-day LIBOR
• The option expires in 128 days
• The exercise rate is 5%
• The notional principal is $40 million
• Current LIBOR = 5.5%
Practice: Example 10, Volume 5, Reading 29
Trang 8Solution:
a)The company will pay $100,000 up front in the
form of option premium
• The rate the firm could earn if it invested the
$100,000 would be 5.5% (i.e current LIBOR
given)
Thus, compounding premium at the
original/current LIBOR of 5.5% + 200 bps for 128
days =
$100,000[1 + (0.055+ 0.02) × (128/360)] = $102,667
• Thus, call premium of $100,000 is equivalent to
$102,667 at the time the loan is taken out
• This increases the cost of the loan because by
paying this amount, the firm effectively receives
= $40 million - $102,667 = $39,897,333
• Thus, effective loan proceeds = $39,897,333
b)The option expires on the date when the loan is
taken out by the company and pays off =
($40,000,000) × Max (0, LIBOR – 5%) × ቀ
• Note that whenever LIBOR is below 5%, the
payoff is zero
• Whenever LIBOR is > 5% e.g when LIBOR is 8%,
the payoff is
($40,000,000) × Max (0, 8% – 5%) × ቀ
$600,000
c)Loan interest = ($40,000,000) × (LIBOR on the date
loan is taken out + 200 bps) × ቀ
For LIBOR = 8%,
Loan interest = ($40,000,000) × (8% + 200 bps) ×
ቀ
ቁ = $2,000,000
d)Effective Interest paid = $2,000,000 - $600,000 =
$1,400,000
e)Effective rate on the loan = {(NP + Effective
interest) / effective loan proceeds} 365 / Days in
underlying rate – 1 = {($40m + $1,400,000) /
$39,897,333}365 / 180 – 1 = 0.0779 = 7.79%
Source: Curriculum, Reading 29, Exhibit 13
Interest rate put options can be used by lenders to
manage interest rate risk on floating-rate loans i.e when
interest rate falls below a specific level, interest rate put
option generates a pay-off for the lender and thus
compensates the lender (e.g bank) for the lower
interest rate on the loan
Example:
A Bank plans to lend $50 million in 47 days at 90-day
LIBOR plus 250 basis points To manage the risk
associated with lower interest rate on a floating-rate
loan, it buys a put option in which the underlying is the rate on 90-day LIBOR
• The option expires in 47days
• The exercise rate is 7%
• The notional principal is $50 million
• Current LIBOR = 7.25%
Solution:
a)The bank will pay $62,500 up front in the form of option premium
• The rate the bank could earn on if it invested the $62,500 would be 7.25% (i.e current LIBOR given)
Thus, compounding premium at the original/current LIBOR of 7.25% + 250 bps for 47 days =$62,500 [1 + (0.0725+ 0.025) × (47 / 360)] =
$63,296
• Thus, put premium of $62,500 is equivalent to
$63,296 at the time the loan is made
• Thus, by paying this amount, the bank loaned =
$50 million + $63,296 = $50,063,296
• Thus, effective amount loaned = $50,063,296 b)The option expires on the date when the loan is made by the bank and pays off =
($50,000,000) × Max (0, 0.07 – LIBOR) × ቀ
payoff is zero
• Whenever LIBOR is < 7% e.g when LIBOR is 6%, the payoff is
($50,000,000) × Max (0, 0.07 – 0.06%) × ቀ
$125,000
c)Loan interest = ($50,000,000) × (LIBOR on the date loan is made + 250 bps) × ቀ
For LIBOR = 6%, Loan interest = ($50,000,000) × (6% + 250 bps) ×
ቀ
ቁ = $1,062,500
d)Effective Interest received = $1,062,500 + $125,000
= $1,187,500
e)Effective rate on the loan = {(NP + Effective interest) / effective amount loan loaned} 365 / Days
in underlying rate – 1 = {($50m + $1,187,500) /
$50,063,296}365 / 90 – 1 = 0.0942 = 9.42%
Source: Reading 29, Exhibit 15
3.3 Using an Interest Rate Cap with a Floating-Rate
Loan Interest rate cap is a combination of interest rate call options where each option’s pay-off occurs on the date
Practice: Example 12, Volume 5, Reading 29
Practice: Example 11,
Volume 5, Reading 29
Trang 9when the interest payments on a loan are due Each
option in a cap is called a caplet
• Each caplet has its own expiration date
• Each caplet has the same Exercise rate
• The cap seller makes payments to the borrower if
interest rates > strike rate during the term of the
cap
• The pay-off of each caplet is determined on its
expiration date, but the caplet pay-off (if any) is
made on the next payment date i.e the date on
which the loan interest is paid
o This implies that if a loan has e.g 6 interest
payments, the cap will contain only five caplets
because there will be only five risky payments as
the first rate on the loan is already set
o A cap will contain six caplets only when the
borrower purchases the cap in advance of
taking out the loan i.e the additional caplet can
be used to protect the 1st rate setting on a loan
Effect of Notional principal amount and exercise
rate/strike rate on cost of cap:
• The cap can be used to protect the entire loan
amount or only a portion of the loan amount
Reducing the dollar amount of the cap results in
reduction of the cost of the cap
• Reducing the strike rate of a cap results in increase
in the cost of the cap
a)Loan Interest payment: It is computed as follows
Loan interest = Notional Principal × (LIBOR on previous
b)Cap Pay-off: It is computed as follows
The cap pay-off = Notional Principal × (0, LIBOR on
previous reset date – Exercise rate) ×
c)Effective Interest = Interest due on the loan – Caplet
pay-off
NOTE:
Since loan has multiple payments, the effective rate on
a loan is similar to IRR on capital investment project or
YTM on a bond
For detail calculations, refer to Exhibit 17, Reading 29
3.4 Using an Interest Rate Floor with a Floating-Rate
Loan Interest rate floor is a combination of interest rate put options where each option’s pay-off occurs on the date when the interest payments on a loan are due to be received Each option in a floor is called a floorlet
• Each floorlet has its own expiration date
• Exercise rate on each floorlet is the same
a)Loan Interest payment: It is computed as follows Loan interest = Notional Principal × (LIBOR on previous
b)Floorlet Pay-off: It is computed as follows The floor pay-off = Notional Principal × (0, Exercise rate -
c)Effective Interest = Interest received on the loan + Floorlet pay-off
For detail calculations, refer to Exhibit 18, Reading 29
3.5 Using an Interest Rate Collar with a Floating-Rate
Loan
A collar is a combination of a long (short) position in a cap and a short (long) position in a floor
The borrower can buy a cap to protect against rising interest rates and sell the floor to finance the premium paid to buy a cap
NOTE:
In this case, effective interest paid in each period will be:
Effective interest paid = actual interest paid – cap pay-off + floor pay-off
by selling the floor can
be used to offset the premium paid to buy a cap
• Buying a cap provides
The lender can buy a floor
to protect against falling interest rates and sell the cap to finance the premium paid to buy a floor
NOTE:
In this case, effective interest earned in each period will be:
Effective interest earned = actual interest earned + floor pay-off – cap pay-off
by selling the cap can
be used to offset the premium paid to buy a floor
• Buying a floor provides
Practice: Example 14, Volume 5, Reading 29
Practice: Example 13,
Volume 5, Reading 29
Trang 10For borrower For lender
protection against rising
interest rates but sale of
the floor results in the
borrower giving up any
gains from interest rates
falling below the
exercise rate on the
floor
•Like Zero-cost collar in
equity options, in
Zero-cost interest rate collar,
first of all borrower
selects exercise rate of
the cap Then, the floor
exercise rate is set such
that the floor premium
offsets the cap premium
so that there is no initial
outlay
protection against falling interest rates but sale of the cap results in the lender giving up any gains from interest rates rising above the exercise rate on the cap
•Like Zero-cost collar in equity options, in Zero-cost interest rate collar, first of all lender selects
exercise rate of the
floor Then, the cap
exercise rate is set such
that the cap premium offsets the floor premium
so that there is no initial outlay
• Typically, in a collar, the call and put premiums
offset each other However, it is not necessarily
always the case
• Zero-cost only means that there is no upfront cash
outlay
Effect of exercise rate and size of notional principal on
cost of hedge: For example in case of long cap & short
floor,
• Initial cost of the hedge can be reduced by increasing the cap exercise rate and decreasing the floor exercise rate; this will result in a decrease
in cost of the cap and generate income from selling the floor However, it will expose the buyer
of collar to more interest rate risk
• Initial cost of the hedge can be reduced by having lower notional principal for the cap and higher notional principal for the floor
A collar creates a band within which the buyer’s effective interest rate fluctuates i.e
• The borrower will benefit when interest rate falls and will be hurt when interest rate increases within that range/band This implies that the borrower will face risk within that range
• Change in interest rate will have no net effect when:
a)Interest rate > cap exercise rate b)Interest rate < floor exercise rate
By trading in options, dealers provide liquidity to the
market and take risk To earn the bid-ask spread without
taking risk, dealers can hedge their positions by using
hedging strategies For example if a dealer has sold a
call, he can hedge his/her risk either by:
i Buying an identical call option or
ii Buying a put with the same exercise price and
expiration, buying the asset, and selling a bond or
taking out a loan with face value equal to the
exercise price and maturity equal to that of the
option’s expiration (it refers to put-call parity) This
hedge is static in nature i.e.no change in the position
is required as time passes
iii.Using Delta Hedging: When necessary options are not
available or are not favorably priced, then the dealer
can hedge risk by taking a long position in a certain
number of units of the underlying asset The size of
that long position is determined using option’s delta
i.e
Delta = ! " #$ %
∆+
• Delta is used to measure the sensitivity of the price
of an option to changes in the price of the
underlying asset
• The delta usually lies between 0 and 1
o Delta will be 1 only at expiration and only if the option expires in-the-money
o During the option’s life, if the option is in-the-money, delta will tend to be above 0.5
o As expiration approaches, the deltas of
in-the-money options will move slowly towards 1.0
o Delta will be 0 only at expiration and only if the option expires out-of-the money
o During the option’s life, if the option is out-of-the-money, delta will tend to be below 0.5
o As expiration approaches, the deltas of
out-of-the-money options will move slowly toward 0
o Delta moves quickly towards 1 or 0 when delta is at-the-money and/or near expiration
o 0.5 is often viewed as an “average” delta
o For calls: delta lies between 0 and 1
o For puts: delta lies between -1 and 0
NOTE:
The deltas of options that are very slightly in-the-money
will temporarily move down as expiration approaches But eventually they will move up towards 1.0
How to determine size of the Long position: Delta can be used to determine how many units of the underlying are
Practice: Example 15, Volume 5, Reading 29