Derivatives-II

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Derivatives – II

www.edupristine.com © Neev Knowledge Management – Pristine 2

• Reading 63: Option Markets and Contracts

• Reading 64: Swap Markets and Contracts

• Reading 65: Risk Management Applications of Option Strategies

Expect around 6 questions in the exam from today’s lecture

Mapping to Curriculum

www.edupristine.com © Neev Knowledge Management – Pristine

Key Concepts

• Calls, Puts and their Payoffs

• Minimum And Maximum Value Of European And

American Options

• Intrinsic And Time Value Of Option

• Covered Call, Protective Put

• Effect Of Variables On Option Pricing

• Option Price Sensitivities

• Interest Rate Caps, Floors, Collars

• Swaps and their Termination

3


Derivatives

• Securities whose price is dependent upon or derived from one or more underlying assets.

• The derivative itself is merely a contract between two or more parties. Its value is determined by

fluctuations in the underlying asset.

• The most common underlying assets include stock, bonds, commodities, currencies, interest rates

and market index.

• Most derivatives are characterized by high leverage.

• Futures contracts, forward contracts, options and swaps are the most common types of derivatives

4


Options

• Seller of an option is also called as option writer

• Option Premium: Price that the owner of an option is required to pay to acquire those rights

5

Options

Call Put

Long Call Short Call Long Put Short Put

Call Buy

Put Sell

The right to

Buy an option

The obligation to

Sell the underlying The obligation to

Buy the underlying

The right to

Sell an option

• Long options have rights

• Short options have obligations


Example: Options And Forward Payoff

If the forward

price at Time 1

is

Payoff for the

forward position

Payoff for Long

Call position

1200 200 200

1100 100 100

1000 0 0

900 -100 0

800 -200 0

6

Forward T=1 Spot T=0

Payoff

S(T)

Forward profit and loss

1000

300

200

100

0

-50

700 800 900 1000

1100 1200 1300

Profit/Loss of the Call

Terminal

stock price ($)

If the Spot price of a computer is $1000.

In the

Money

Out of

the

Money

At the

Money


Long Call

• Profit from buying one European call option: option price = $5, strike price = $100, option life = 2

months

7

30

20

10

0

-5

70 80 90 100

110 120 130

Profit ($)

Terminal

stock price ($)


Short Call

• Profit from writing one European call option: option price = $5, strike price = $100

8

-30

-20

-10

0

5

70 80 90 100

110 120 130

Profit ($)

Terminal

stock price ($)


Long Put

• Profit from buying an European put option: option price = $7, strike price = $70.

9

30

20

10

0

-7

70 60 50 40 80 90 100

Profit ($)

Terminal

stock price ($)


Short Put

• Profit from writing an European put option: option price = $7, strike price = $70

10

-30

-20

-10

7

0

70

60 50 40

80 90 100

Profit ($) Terminal

stock price ($)


Payoffs From Options

11


Types Of Options

• Financial Options:

– Based on Equity, Indices, Bonds, interest rates, currencies

– Equity Options:

• Most popular

– Index Options:

• European Style

• Settled in cash

– Bond Options

• Mostly traded OTC and only a few exchanges.

• Liquidity of the Government Security market is much larger than the corporate bond market.

• Options almost always on Government Securities

• Can be either European or American

• Expiration date must be much before the underlying’s maturity date since the price tends to be very close to

par value at expiration. Else, it removes much of the uncertainty in its price.

– Currency Options

• A currency option allows the holder to buy (if a call) or sell (if a put) an underlying currency at a fixed exercise

rate expressed as an exchange rate.

• Usually traded OTC, but there are a few exchanges trading them with low activity

12


Types Of Options (Continued)

• Options on futures:

– Call => option to go long a future contract

– Put = > option to go short a future contract

• Commodity Options:

– Gives the holder the right to buy/sell the underlying commodity at the strike price

• Real Options are options to be taken into account while doing NPV analysis

– E.g. option to abandon a project before completion

13


Question

• Which of the following single option transaction can be most risky?

A. Writing a put

B. Buying a put

C. Writing a call

14


Solutions

• C.

– As the stock price of the underlying increases above the exercise price of a call option, writer of the option

faces unlimited risk whereas buyer of the option face unlimited gain in this situation.

15


European & American Options

16

Options Type

European

Options

American

Options

Can be exercised

only at the end of

its life

Option Premium

Is Lower

Can be exercised

at any time before

or on expiration

Option Premium

is Higher


Minimum And Maximum Value Of European And American

Options

17

• c : European call option price

• p : European put option price

• S0 : Stock price today

• X : Strike price

• T : Life of option

• σ: Volatility of stock price

• C : American Call option price

• P : American Put option price

• ST : Stock price at option maturity

• D : Present value of dividends during

option’s life

• r : Risk-free rate for maturity T with

continuous compounding

Notations


Minimum And Maximum Value Of European And American

Options (Cont…)

• An American option is worth at least as much as the corresponding European option

– C ≥ c

– P ≥ p

18

Type Lower Bound Upper Bound

European Call 0 St

American Call 0 St

European Put 0 X / (1 + RFR)(T-t)

American Put 0 X


American Options, Lower Bounds, Early Exercise

• American Options can be executed earlier than expiration which can have value.

• Hence,

C0≥c0

P0 ≥p0

• There is no real reason to execute a call option early because:

– You lose interest on your money

– You lose the insurance.

• Exceptions

– If there is a cash payment, like dividend payments

• For American Puts, there is always a possibility of early exercise

– Especially when the underlying price is low or in case of bankruptcy.

19


Bounds Revised

Revised Table:

20


European Call Max[0, St - X / (1 + RFR)T-t] St

American Call Max[0, St - X / (1 + RFR)T-t] St

European Put Max[0, X / (1 + RFR)T-t - St ] X / (1 + RFR)(T-t)

American Put Max[0, X – St ] X

CallEuropean CallAmerican

PutEuropean PutAmerican

Imp

Total Value of option

Intrinsic Value


Example

• Find lower bound for American and European put X = $45, stock is trading at $42, RFR = 6%, 3

months expiry

– American: Max[0,45 - 42] = $3

– European: Max[0, 45/1.063/12 – 42] = $2.34

• Find lower bound for American and European call X = $45, stock is trading at $49, RFR = 6%, 3

months expiry

– American=European: Max[0, 49 – 45/1.063/12 ] = $4.65

21


Questions

1. Maximum value for European Put and American Put is if “X” is strike price, “S” is spot price, “RFR” is

risk free rate and “T” is time to maturity of the contract –

A. European Put: X/(1 + RFR)T-t, American Put: X

B. European Put: X, American Put: X/(1 + RFR)T-t

C. European Put: X, American Put: X

2. What are the minimum values of an American-style and a European-style 3-month call option with a

strike price of $90 on a non-dividend-paying stock trading at $96 if the risk-free rate is 3%?

A. American: $6.00, European: $6.00

B. American: $6.00, European: $5.62

C. American: $6.62, European: $6.62

3. The minimum value of a American put option is:

A. Max[0, X – St ]

B. Max[0, St - X / (1 + RFR)T-t]

C. Max[0, X / (1 + RFR)T-t - St ]

4. Which of the following is closest approximation for the maximum value of a call option

A. The price of the stock minus the exercise price

B. The exercise price times one plus the risk free return

C. The price of the stock

22


Questions

5. European and American options differ in the way that

A. American option can be exercised any time till expiry, European can not be exercised before expiry

B. European option can be exercised upto 10 days before expiry, American can not be exercised before

expiry

C. European option can be exercised any time till expiry, American can not be exercised before expiry

6. A European call option on an underlying asset has a strike price of $ 120 and a time to expiration of

0.25 years. Risk-free rate is 6 percent. If the underlying asset is trading at $140 then which of the

following represents the lower bound for the call option:

A. $20

B. $21.74

C. $17.98

23


Solutions

1. A.

2. C.

3. A.

4. C.

5. A.

6. B.

Lower of a European call option

= Max (0, S – X/(1+RFR)T)

= $21.74

24


Intrinsic And Time Value Of Option

• Intrinsic value: It is amount by which the option is in-the-money

• Intrinsic value of a call option; C = max[ 0, S – X ]

• Intrinsic value of a put option; P = max[ 0, X - S ]

• Example: If the stock price is say, $25, and the exercise price is $20. The intrinsic value of the option

is $5.

• At-the-money and Out-of-the money options do not have any intrinsic value

• Time value of a option:

– Portion of the option premium that is attributable to the amount of time remaining till maturity

– Longer the time to maturiy, higher is the time value of the option

• Total Option Value = Intrinsic value + Time Value

25


Moneyness Of An Option:

26

Out-of-The-Money

At-The-Money

Stock price

In-The-Money


Call Option Profit & Losses

• Consider a call option:

– Premium = $5

– Strike price = $50

– Profit (p)

– = Max(0,ST-X) – c0

– Max Profit =

– Max Loss = c0

27

Profit

Long Call

Breakeven

(X+ premium)

Short Call

Stock Price X= $50 $55

+$5

-$5

0


Put Option Profit & Losses

• Consider a put option:

– Premium = $5

– Strike price = $50

– Profit (p)

– = Max(0,X-ST) – p0

– Max Profit = X-p0

– Max Loss = p0

28

Profit

$45

$5

0

-$5

-$45

$45 X= $50

Short Put

Long Put

Stock price

Breakeven(X - Premium)


Questions

1. If the owner of a call option with a strike price of $35 finds the stock to be trading for $42 at

expiration, then the option:

A. Expires worthless.

B. Will not be exercised

C. Is worth $7 per share.

2. What is the option buyer's total profit or loss per share if a call option is purchased for a $5 premium,

has a $50 exercise price, and the stock is valued at $53 at expiration?

A. ($5)

B. ($2)

C. $3

3. A put option with strike price of $20 has an option premium of $2. At expiry, underlying was traded at

$22. Premium at expiry day would be

A. $2

B. $1

C. None of the above

29


Questions

4. What is the worst-case profitability scenario for an investor who sold a call on the firm's stock for a

premium of $10 and a strike price of $100?

A. $90 per share profit

B. $0 per share profit (break-even)

C. Unlimited losses

5. An investor buys a put on a stock selling for $80, with a strike price of $75 for a premium of $6. The

maximum gain is :

A. $70

B. $69

C. $75

6. A person faces highest risk of maximum loss if he trades -

– Write unprotected Call

– Buy unprotected Put

– Write unprotected put

30


Solutions

1. C.

2. B.

3. C.

4. C.

5. B. The maximum gain is = $75(strike) - $6(premium) = $69

6. A

.

31


Agenda

• Option Markets and Contracts

• Risk Management Applications of Option Strategies

• Swap Markets and Contracts

32


Covered Call = Long Stock + Short Call

• Involves selling call options of stocks already owned or simultaneously bought

• Motivation

– Earning a return from the underlying that is already owned

– Lowering the cost of acquisition of the underlying asset

• Expectation

– Moderate rise in the price of the underlying

• Profit Potential

– Maximum Profits when the options are exercised by the buyer

• Premium received + Strike Price – Spot Price

– If the options are not exercised the trader gets to keep the premium, thus lowering the cost of acquiring

the asset

• More conservative than buying the stock only

33


Covered Call = Long Stock + Short Call

• Value at expiration: VT = ST – Max(0,ST-X)

• Profit: p= VT - S0 + c0

• Maximum Profit

X – S0 + c0

• Maximum Loss

S0 – c0

• Breakeven

S0 – c0

34

profit

(loss)

underlyin

g

price

0

profit

(loss)

underlying

price

0

profit

(loss)

underlying

price

0 +

=

Buying the Underlying Sell Call

Covered Call spread


Covered Call = Long Stock + Short Call (Cont…)

• If My Company(MC) trades at Rs33 and Rs35 calls are priced at Rs1, then an investor can purchase

100 shares of MC for Rs3300 and sell one (100-share) call option for Rs100, for a net cost of only

Rs3200. The Rs100 premium received for the call will cover a Rs1 decline in stock price. The break-

even point of the transaction is Rs32/share. Upside potential is limited to Rs.300, but this amounts to

a return of almost 10%. (If the stock price rises to Rs35 or more, the call option holder will exercise his

option & the investor's profit will be Rs35-Rs32 = Rs3). If the stock price at expiry is below Rs35 but

above Rs32, the call option will be allowed to expire, but the investor can still profit by selling his

shares. Only if the price is below Rs32/share will the investor experience a loss.

35

Stock price

at expiration Net profit/loss

Comparison to

simple stock

purchase

Rs.30 (200) (300)

Rs.32 0 (100)

Rs.33 100 0

Rs.35 300 200

Rs.37 300 400


Protective Put = Long Stock + Long Put

• Involves buying put options of stocks already owned or simultaneously bought

• Motivation

– Protection against loss in the value of stocks owned

• Expectation

– Rise in the price of the underlying

• Advantage

– Trader profits from the rise in price of the underlying albeit the amount of profit is reduced by the premium

paid to purchase the put

– In case the price of the underlying goes down, the trader is still able to sell the underlying at the strike

price, thus insuring her profit

36


Protective Put = Long Stock + Long Put

37

Protective Put Strategy:

• Long a Stock.

• Long a Put Option.

• The payoff diagram of this strategy

would be look like a Long Call.

• Value at expiration VT = ST + Max(0,X -

ST)

• Profit: p = VT – S0 – p0

• Maximum Profit

=

• Maximum Loss

= S0 + p0 – X

• Breakeven

= S0 + p0

Profit

ST

K


Role of Arbitrage

• Arbitrage refers to riskless profit

• Such profits are generally earned when securities are mispriced

• Example: Short-selling a stock which is mispriced high in one market and simultaneously buying it in another

market where the same security is priced lower

• When several market participants enter arbitrage transactions, securities return to their fair values

• Arbitrage plays an important role in valuing securities

• Types:

– Law of one price states that securities with Identical cash flows must have the same price

– Portfolio of securities (with uncertain individual returns) has a certain payoff ==> then the portfolio should

give risk free rate of return

38


Share Price at

Expiration

Call

Pay-Off Strike Price

Bond Value at

Maturity Bond + Call

0 - 5 0 5 5 5

6 1 5 5 6

7 2 5 5 7

8 3 5 5 8

9 4 5 5 9

10 5 5 5 10

Put Call Parity

• Consider the Pay-off of a trader who has the following position:

– A Call Option with a Strike Price of 5 and,

– A Bond with a maturity value of 5.

39


Share Price at Expiration Put Pay-Off (Exercise Price 5)

Stock

Pay-off

Stock+

Put

0 5 0 5

1 4 1 5

2 3 2 5

3 2 3 5

4 1 4 5

5-10 0 5-10 5-10

Put Call Parity

• Consider, now, the Pay-off of a trader who has :

– A Put Option with a Strike Price of 5 and,

– An equivalent unit of the underlying asset

40


0

2

4

6

8

10

12

0 2 4 6 8 10 12

Share Price

TotalPay-off

Put Call Parity

• The Pay-offs are exactly the same

41


Put Call Parity is valid only for European options, for American Options this relationship

turns into an inequality

The Pay-offs Are Exactly The Same

• Put Call parity provides an equivalence relationship between the Put and Call options of a

common underlying and carrying the same strike price:

• It can be expressed as:

– Value of call + Present value of strike price = value of put + share price.

42

Sp

RER1

Xc

T


Questions

1. Suppose an investor buys one share of stock and a put option on the stock. What will be the value of

her investment on the final exercise date if the stock price is below the exercise price?

A. The value of two shares of stock

B. The value of one share of stock plus the exercise price

C. The exercise price

2. An investor shorts 100 shares of a company at $50 per share and at the same time writes a put

option of the same company with a strike price of $48 for a price of $4 per share. If the spot price of

the stock on the expiration date is $52. What is the maximum profit/loss to the writer of this covered

put option?

A. 0

B. $200 profit

C. $400 loss

3. An investor writes a covered call with the exercise price of $55 and the current value of the asset as

$50.The premium charged for writing the call is $ 4. Then which of the following statements does not

reflect the gain/loss of the investor.

A. Investor can a loss of $ 48.

B. Investor can make a gain is $8

C. Investor can suffer a loss of $45

43


Questions

4. An investor writes a covered call with the exercise price of $55 and the current value of the asset as

$50.The premium charged for writing the call is $ 4. Then which of the following statements does not

reflect the gain/loss of the investor.

A. Investor can a loss of $ 48.

B. Investor can make a gain is $8

C. Investor can suffer a loss of $45

44


Solutions

1. C.

2. B.

– The put option would not be executed and the writer of the put gets the premium of $ 400. But since it is a

naked call option, the investor has to buy the shares in the spot market at $52 and close his short

position. In this transaction he makes a profit of $200 (5000+400-5200)

3. A.

– The breakeven value of the asset’s price for the investor is $46. The option will be exercised when the

asset value moves above $55. So the investor can make any gain up to $9. If the asset price falls below

$46 then the investor will make a loss but maximum loss can be $46 when the asset price is zero.

4. A.

– The breakeven value of the asset’s price for the investor is $46. The option will be exercised when the

asset value moves above $55. So the investor can make any gain up to $9. If the asset price falls below

$46 then the investor will make a loss but maximum loss can be $46 when the asset price is zero.

45


Effect Of Variables On Option Pricing

46

c p C P Variable

S0

K

T

σ

r

D

+ + – + ? + +

+ + + + + – + –

– – – +

– + – +

(S-X) (S-X) (X-S) (X-S)

Imp

?


Questions

1. Which of the following will most likely increase the value of a European put option?

A. Decrease in the exercise price

B. Increase in volatility of an asset or interest underlying the option.

C. Increase in the time to expiration.

2. The value of a European put option:

A. Increases with an increase in both volatility and discount rate

B. Increases with an increase in volatility but decreases with an increase in discount rate

C. Decreases with increase in both volatility and discount rate

47


Solution

1. B.

– A decrease in the exercise price of a put option( both American and European) decreases its

value. We cannot positively state that the value of a European put will increase with longer

maturity. However increase in the volatility of an asset or interest underlying the option will

increase the value of both the American and European Call and Put options.

2. B.

– The value of European put option is directly related to volatility and inversely related to the discount rate.

48


Example: An Arbitrage Opportunity?

• Suppose that

– c = 3 S0 = 20

– T = 1 r = 10%

– X = 18 D = 0

Is there an arbitrage opportunity?

49


Questions

1. European put-call parity says the difference in price for call options less put options, both with

exercise price E and time to maturity T, is equal to the stock price:

A. Minus the future value of the exercise price.

B. Plus the future value of the exercise price.

C. Minus the present value of the exercise price

2. A stock is selling at $ 50; a 3 months call at $ 60 is selling for $2 whereas a 3 months put at $60 is

selling for $ 14.The risk free rate is 6%. Considering these figures the gain which can be made

through arbitrage is:

A. $2.87

B. $ 2

C. $ 0 ( No arbitrage possible)

3. Which of the following is not a characteristic of a fiduciary call?

A. Consists of a combination of a call option and a pure-discount, riskless bond that pays the same

amount as the exercise price of the call option.

B. The payoff is equal to stock price of the underlying asset when the call is in money.

C. It consists of a share of a stock together with a call option on the stock.

50


Questions

4. A protective put is best described by:

A. Long European put on a stock + Long the stock

B. Long European put on a stock + Short the stock

C. Short European put on a stock + Long the stock

5. Which of the following statements is true?

A. For both calls and puts an increase in the exercise price will cause an increase in the option price

B. For both calls and puts an increase in the time to maturity will cause an increase in the option price

C. For calls, but not for puts, an increase in the time to maturity will cause an increase in the option price

6. Which of the following statements are true:

A. Longer the time to maturity lesser is the value of the option.

B. Call prices are directly related to the exercise price.

C. The value of an option cannot be negative

51


Questions

7. If the volatility of the underlying asset decreases, then the:

A. Value of the put option will increase, but the value of the call option will decrease

B. Value of the put option will decrease, but the value of the call option will increase

C. Value of both the put and call option will decrease

8. Which of the following features increase(s) the value of a call option?

A. A high interest rate

B. A highly variable stock price

C. All of the above

52


Solutions

1. C.

2. A.

– If the put –call parity equation does not hold true then there is a chance of arbitrage. The synthetic stock

price is given by S = C-P +X/(1+RFR)T

Where C = $2

P = $14

X =$60

RFR = 6% and T =0.25 years

Synthetic Price S = 47.13

Since the stock is selling for $50 so you can immediately short a share for $50 and buy a synthetic for an

immediate arbitrage profit of $2.87.

3. C. – Fiduciary call consists of a combination of a call option and a pure-discount, riskless bond that pays the

same amount as the exercise price(X) of the call option. The payoff is equal to stock price of the

underlying asset when the call is in money, and equal to exercise price when the call is out of money.

4. A.

5. B

6. C

7. C

8. C

53


Agenda

• Option Markets and Contracts

• Risk Management Applications of Option Strategies

• Swap Markets and Contracts

54


Interest Rate Caps, Floors, Collars

• Interest rate cap: Puts a cap on the maximum interest rate the floating rate borrower will have to pay

in the event of increase in interest rates.

– Series of call options

– Which have expiration dates corresponding to the reset dates of a floating rate loan

– Protects a floating rate buyer against an increase in interest rates

– Each component call option called a caplet

• Interest rate floor: Specifies the minimum interest rate the floating rate lender will receive in the event

of decrease in interest rates.

– Series of put options

– Which have expiration dates corresponding to the reset dates of a floating rate loan

– Protects a floating rate lender against a decrease in interest rates

– Each component put is a floorlet.

55


Interest Rate Collars

• Interest Rate Collar is constructed by either

1. Long Cap and Short Floor

2. Short Cap and Long Floor

• If their premiums offset each other, it is called a Zero-Cost Collar.

56


Question

• The pay off for which of the following is most likely equivalent to that of a series of put options?

A. Interest Rate Cap

B. Interest Rate floor

C. Interest Rate Collar

57


Solution

• B.

58


Characteristics Of Swaps

• A swap is an agreement to exchange cash flows at specified future dates according to certain

specified rules:

– Interest Rate Swaps

– Currency Swaps

• Traded mostly OTC and are customized to suit the needs of the parties to the contract

• Subject to default risk.

• Netting – Exchanging only the net amount owed from one party to the other. Netting payments

decrease default risk.

• A swap has zero value at the initiation of the contract.

59


Characteristics Of Swaps

• Interest rate Swaps do not require the actual exchange of the notional amount of the contract

• Currency Swaps requires the exchange of principal in the respective currencies on initiation and

termination of the contract

• Swaps act as a good hedge instrument.

• Settlement/Payment Date: Each date the party makes payments.

• Settlement Period: The time between Settlement Dates

• Termination Date: The final payment date

• Tenor: The original maturity of the swap.

60


Termination Of Swaps

• Ways to terminate the contract before maturity:

– Mutual Termination

– Offsetting contract

– Resale of Swap to another party

– Swaption

61


Plain Vanilla Interest Rate Swap

• An agreement by Microsoft to receive 6-month LIBOR & pay a fixed rate of 5% per annum every 6

months for 3 years on a notional principal of $10 million

Uses of an Interest Rate Swap

• Converting an investment return or liability from

– Fixed rate to floating rate

– Floating rate to fixed rate

62

Period Libor rate Floating Leg Fixed Leg Net Cash Flow

0 4.20% 210,000 250,000 (40,000)

1 4.80% 240,000 250,000 (10,000)

2 5.30% 265,000 250,000 15,000

3 5.50% 275,000 250,000 25,000

4 5.60% 280,000 250,000 30,000

5 5.90% 295,000 250,000 45,000

6 6.40% 320,000 250,000 70,000

Net (For fixed rate payer) = (Swap fixed rate – LIBOR) (No. of days/360) (Notional Principal)


Equity Swap

• Equity Swaps: It refers to an arrangement where one party pays the returns received on the stock or a

stock index in exchange for a return imitating a fixed rate or a floating rate bond

• It has two distinct features

– The party paying fixed could also have to be paying variable. This is in the case where equity returns are

negative

– Both the parties are uncertain about the payments they will receive untill the settlement date.

• For some swaps, the equity returns may be comprised of both dividends and capital gains.

63


Questions

1. For which of the following type of contracts is the payment due/receivable by the parties to the

contract not netted against each other

A. Interest Rate Swaps

B. Equity Swaps

C. Currency Swaps

2. The unique feature of Floating for return Equity Swaps is that:

A. It involves exchange of return on equities

B. It is very easy to value

C. Both parties are uncertain about the return they will receive

3. Which of the following is least likely correct?

A. The notional principal is swapped at inception and at termination of a currency swap

B. In an interest rate swap only interest rate is exchanged

C. Only the net difference between the dollar interest and the foreign interest is exchanged in a currency

swap.

64


Questions

4. Bank A enters into a $10,000,000 million quarterly pay plain vanilla interest rate swap as the fixed

rate payer at a fixed rate of 5% based on a 360 day year. The floating rate payer agrees to pay 90

day LIBOR plus 1% margin; 90 day LIBOR is currently 4%.90 day LIBOR 90 days from now is 5%

and 180 days from now is 5.5%. What amount Bank A pays or receives?

A. $0 pay

B. $50,000 pay

C. $50,000 receive

5. Which of the following is most likely a characteristic of a plain vanilla interest swap in a single

currency?

A. Notional principal is swapped at initiation.

B. Interest payments are netted out and net amount is paid by one who owes it.

C. At the term of the contract notional principals are netted out and the net amount is paid by the one

who owes it.

6. An agreement by Microsoft to receive 6-month LIBOR & pay a fixed rate of 5% per annum every 6

months for 3 years on a notional principal of $10 million. What is the net cash flow in period 3 if 6-

month LIBOR at start of period 3 is 5.5%?

A. $275,000

B. $250,000

C. $25,000

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Questions

7. Which of the following is least likely a characteristic of Swaps?

A. They are customized contracts

B. They are traded in organized secondary market

C. Most participants in swaps market are large institutions.

8. The major risk with Swaps is:

A. Liquidity risk

B. Counterparty risk

C. Market risk

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Solutions

1. C.

2. C.

3. C.

4. C.

– Bank A pays = [0.05*(180/360) – (0.05 + 0.01)(180/360)]*10,000,000 = - $50,000, so receives $50,000.

5. C. – In a plain vanilla interest swap in a single currency the following steps takes place:

• Notional principal is generally not swapped at initiation in single currency swaps.

• Full interest payments are exchanged at each settlement date, each in a different currency

• Since a notional fund was not swapped, there is no transfer of funds.

6. C.

7. C They are traded in organized secondary market. Swaps are customized contracts which are not

traded in any organized secondary market.

8. B.

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Interest Rate Option Payoff

• Payoff for other types of options is simple

• Example: For the holder of a call option, he will receive the amount by which the current stock price is higher

than the exercise price on the expiry of the contract

• The payoffs in case of interest rate options is received not on expiry of the contract but on expiry of the

period for which the notional amount is borrowed at the reference rate

• Example:

XYZ bought a 30-day call option on a 120-day LIBOR. The notional principal is $ 1,00,000 and the strike rate

is 6%. If the 120-day LIBOR on expiry is 7% on expiry of the option contract what is the payoff to XYZ.

• Solution:

Interest Saved = (0.07 - 0.06) (1,00,000) (120/360)

= $333.33

But this amount will be received after 120 days after the expiry of the option contract

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Purpose Of Derivative Markets

• Purpose of Derivatives:

• Risk Management: It is a process of identifying the desired level of risk, identifying the actual level of

risk, & altering the latter to equal the former. Hedging & speculation are the two processes here

– Hedging & speculation: is a process generally refers to the reduction, & in some cases the elimination of

risk

– Hedging: involves taking an offsetting position in a derivative in order to balance any gains and losses to

the underlying asset.

• Hedging attempts to eliminate the volatility associated with the price of an asset by taking offsetting positions

contrary to what the investor currently has

• Hedgers reduce their risk by taking an opposite position in the market to what they are trying to hedge

• The ideal situation in hedging would be to cause one effect to cancel out another

• protect itself from any downside risk

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Purpose Of Derivative Markets (Cont…)

– Speculators: They make bets or guesses on where they believe the market is headed

• Example, if a speculator believes that a stock is overpriced, he or she may short sell the stock and wait for the

price of the stock to decline, at which point he or she will buy back the stock and receive a profit

• Speculators are vulnerable to both the downside and upside of the market; therefore, speculation can be

extremely risk

• The main purpose of speculation is to profit from betting on the direction in which an asset will be moving

– Price Information: Futures markets provide valuable information about the prices of the underlying

assets on which futures contracts are based

• Many of the assets are traded in geographically dispersed regions, thus many different spot prices exist

• Price of contract with shortest time to expiration often serves as a proxy for the price of underlying asset

• Prices of all future contracts serve as prices that can be accepted by those who trade contracts in lieu of

facing the risk of uncertain prices

• Forward contracts & swaps also allows users to substitute a single locked-in price for the uncertainty of future

spot prices

– Reduce transaction costs: Derivatives are characterized by relatively low transaction costs

• Because derivatives are designed to provide a means of managing risks (thus, it serve as a form of

insurance)

• Insurance cannot be viable if its price is too high relative to the value of insured asset

• Thus, derivatives must have low transaction costs otherwise they would not exist

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Criticism Of Derivatives

• Criticism of Derivatives:

• They are very complex, sometimes the users don’t understand them well

• Too risky (leverage)

– Example: Margin trading -> using leverage form the broker to buy the securities

• Mistakenly characterized as a form of legal gambling

• Important distinction between derivatives & gambling is:

– Benefits of derivatives extent much further across society

– By providing the means of managing risk, they make financial markets work better

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Questions

1. Which of the following type of options gives the holder the right to buy/sell the underlying commodity

at the strike price?

A. Real Options

B. Commodity options

C. Financial options

2. What is least likely to be true regarding financial derivatives

A. Derivatives create excess financial risk in the system

B. Derivatives are used for speculation

C. Derivatives helps in price discovery of underlying

3. Which combination of positions will tend to protect the owner from downside risk?

A. Buy the stock and buy a call option.

B. Sell the stock and buy a call option.

C. Buy the stock and buy a put option.

4. Which combination of positions is least likely to protect from risk of stock price going up down?

A. Buy the stock and buy a call option.

B. Sell the stock and buy a call option.

C. Buy the stock and buy a put option.

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Solutions

1. B.

2. A.

– On the contrary derivatives are meant to transfer the risk on to a party, which is better equipped to

handle and mitigate it. However derivatives are also used for speculation and they help in price discovery

by increasing liquidity.

3. C.

4. A.

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Interest Rate Options Versus FRAs

• Interest rate Option: It is an option which gives the holder the right to go long/short on a notional

amount at the strike interest rate for a fixed period

• Combination of a long interest rate call option and a short interest rate put option will give the same

payoff as a long position in an FRA

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Rate Options

– LIBOR – considered the best measure of an interest rate paid in dollars on a non governmental borrower.

– FRA’s

• Forward contracts that pays off based on the difference between the underlying rate and the fixed rate

embedded in the contract when it is constructed.

• The payoff is discounted by the spot rate on a 180-day LIBOR to give the present value for the payoff as of

the expiration date.

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Rate Options

– Interest Rate Option

• Has an exercise rate or strike rate

• It is the right, not obligation, to make one interest payment and receive another.

• Interest Rate Calls and Interest Rate Puts

• Settled in cash

• Mostly European but can be American too

• The money is not paid at expiration, but paid at a later date (no need to discount payment)

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Questions

1. Forward rate agreement (FRA) has the same payoff as a combination of:

A. Long interest call option and short interest put option

B. Short interest call option and long interest put option

C. Long interest call option and Long interest put option

2. Payoff of a long position in an FRA is the same as a combination of:

A. Long interest rate call option and a short interest rate put option

B. Short interest rate call option and a short interest rate put option

C. Short interest rate call option and a long interest rate put option

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Solutions

1. A.

– Forward rate agreement (FRA) has the same payoff as a combination of long interest call option and

short interest put option.

2. A.

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Five Minute Recap

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European Call Max[0, St - X / (1 + RFR)T-t] St

American Call Max[0, St - X / (1 + RFR)T-t] St

European Put Max[0, X / (1 + RFR)T-t - St ] X / (1 + RFR)(T-t)

American Put Max[0, X – St ] X

c p C P Variable

S0

K

T

σ

r

D

+ + – +

+ ? + + + + + + + – + –

– – – +

– + – +

(S-X) (S-X) (X-S) (X-S)

Interest Rate Collar is constructed by

either

1. Long Cap and Short Floor

2. Short Cap and Long Floor

Swap Characteristics:

• Traded mostly OTC - customized

• Subject to default risk.

• Usually Netted - decrease default risk.

• Zero value at the initiation of the contract.

• Interest rate Swaps - do not require the actual exchange of

the notional amount

• Currency Swaps - requires the exchange of principal in the

respective currencies on initiation and termination of the

contract

• Equity Swaps – Fixed paying might need to pay floating in

case of a negative equity return,

Swap Terminology

Settlement/Payment Date: Each date the party makes payments.

Settlement Period: The time between Settlement Dates

Termination Date: The final payment date

Tenor: The original maturity of the swap.

Swap Termination before maturity:

• Mutual Termination

• Offsetting contract

• Resale of Swap to another party

• Swaption

Sp

RER1

Xc

T

Call Put Parity

Derivatives-II

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Transcript of Derivatives-II