futures and options- a primer

8/7/2019 Futures and Options- a Primer

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PRESENTATION ON

FUTURES AND

OPTIONS

BY

A.V. VEDPURISWAR


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INTRODUCTION TO

FUTURES What are futures?

Locking in Right and obligation till contract is

cancelled

Originated in the case of commodities

Clearing House

Different from forwards


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Differences between futures and

forwards Inter Bank vs Exchange

Standardized vs Tailor made

Marking to market

Inexact compensation

Variability in interest rates Marking to market risk

Non matching of contract size, maturity


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MARGIN Guarantee

Based on daily variation

Near month contracts - More margin

Hedger vs Speculator

Spread vs Open Day vs Position

Volatility- 1987 S & P 500- $6000-50,000


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Investor----Broker-----CH member---CH

Initial, Maintenance Cash, T Bills(90%), Shares(50%)

Inter market cross margining

Mean + 3 X Std devn


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CLEARING ASSOCIATION Clearing association sets

minimum capital requirements

position limits

price limits

Organisation

CBOT : Separate affiliated corporation

CME, NYME : Part of exchange


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DELIVERY Futures referred to by delivery month

Delivery period clearly specified by

exchange

Closest month- Front/Spot month

Further month-Back month


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LIQUIDATION OF

CONTRACT Physical delivery Trader--FCM--C.H

Offsetting Report to Clearing House

Exchange of futures for physical

Delivery outside exchange

Flexibility- Time, place, substitute

Cash delivery- Stock Index futures

Difficulty in delivery/Shortage of commodity


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Impact of trading on Open

InterestTime Trading Open Interestt=0 Trading starts 0

t=1 A buys one contract 1

B sells one contract

t=2 C buys three contracts 1+3

D sells three contracts =4

t=3 A sells one contract 4-1D buys one contract =3

t=4 C sells one contract 3+1-1

E buys one contract = 3


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Operational aspects1. You can withdraw any balance in the margin

account in excess of the initial margin

2. If the amount falls below the maintenancelevel, it has to be topped up to the initial margin

level

3. In most cases, it is more convenient to use

offsetting transaction than deliver


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Contract sizes on Chicago

Mercantile ExchangeCurrency Contract size

Australian Dollar 100,000

Brazilian Real 100,000

British Pound 62,500

Canadian Dollar 100,000Deutsche Mark 125,000

E.C.U 125,000


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FUTURES AND FORWARD PRICES

If futures prices are positively correlatedwith interest rates, a long trader will prefer afutures position to a forward position

Both the futures and forward contracts willhave the same profit in the end exclusive ofdaily settlement payments. If the futuresposition generates more favourable interimcash flows due to its positive correlationwith interest rates, then the futures priceshould exceed the forward price.


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If futures prices are inversely correlated

with interest rates, the futures price will beless than the forward price

If the price of a commodity is unrelated tointerest rates, forward and futures prices

should be equal.


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RELATIONSHIP BETWEEN SPOT

PRICES AND FUTURES PRICES

COST OF CARRY MODEL

Futures prices depend on the cash price of a

commodity and the cost of storing the underlyinggood from the present time to the delivery date

Carrying cost :

storage

insurance

transportation

financing


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Rule 1 : F0,t = S0(1+c)

Otherwise, we can go short in underlying, invest

the cash so obtained, buy futures, take delivery

and square up short position

Rule 3: F0,t = S0(1+c)


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Rule 4: F0d = F0,n

(1+c)

Otherwise, sell nearby contract, deliver by

borrowing, buy distant contract and square up

earlier short position

Rule 6: F0d = F0,n(1+c)


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LIMITATIONS

TRANSACTION COSTS RESTRICTIONS ON SHORT SELLING

BORROWING AND LENDING RATES

MAY NOT BE EQUAL

SOME GOODS ARE PERISHABLE AND

CANNOT BE STORED


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F0,t = S0 (1 - T)(1 + C) Short in Spot Market

S0 (1 - T)(1 + C)


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MECHANICS OF HEDGING A. Payables Exposure Buy futures now

Sell futures on maturity

Buy spot on maturity

B. Receivables Exposure

Sell futures now

Buy futures on maturity

Sell spot on maturity


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PRINCIPLES OF

SPECULATION

Observe market trends

Take opposing / differing position

Risk loving speculator Open position

Risk averse speculator Spread position


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DAILY SETTLEMENT : AN

EXAMPLE Tuesday : Investor takes long position in SF futures

Price = $ 0.750 Size = SF 125,000

Next day, Price = $ 0.755 Gain in margin account = 125,000(0.755-0.75)= $ 625

Existing futures contract is canceled. New contract

takes shape at $ 0.755

Next day, Price = $ 0.752 Loss in margin account =125,000(0.755-0.752)= $375

Next day, Price = $ 0.740

Loss = 125,000(0.752-0.740) = $1500


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ILLUSTRATION

October Soyabean Oil futures are selling at 19.44cents/pound. The standard size of the contract is

60,000 lb.The initial margin requirement is

$3000 and the maintenance margin, $1500. If a

trader goes long in two October futures contracts

and the prices on the subsequent four days are

19,19.4,19.6 and 19.8 cents/lb explain how the

margin account changes. Assume that money inexcess of the initial margin is withdrawn

immediately.


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Solution

Day Change Change in Margin Margin Balance

in Price Contract Call Withdrawal ($)

Value ($) ($) ($)

1. - 0.44 -528 - - 5472

2. +0.40 +480 - - 5952

3. +0.20 +240 - 192 6000

4. +0.20 +240 - 240 6000


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ILLUSTRATION

A trader feels that the Mexican Peso is undervalued and

decides to speculate by trading in ten standard futures of

size MP 1,000,000. The contracts are trading at $0.0435.

When the trader closes out, the futures are quoting at$0.0430. What are the traders gains/losses?


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Solution

Buy futures

Profit = (0.0430 -0.0435)(10)(1,000,000)

= - $ 5000


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ILLUSTRATION

On April 1, 1996, a speculator has collected the followingquotes ($/100 yen)

Spot : 0.7796 June : 0.7580 Sep: 0.7600

Dec : 0.7690 Mar: 0.7710

The speculator feels that the US inflation rate is going to

accelerate in view of the Feds looser monetary policies and

the yen could appreciate strongly towards the end of the

year. What strategy can she adopt? If on December 7, thequotes are as follows, what profit would she have earned?

Dec : 0.7825 Mar : 0.7885


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SOLUTION Buy March Sell December

Opening : -0.7710 +0 .7690 = -0.002

Closing : +0.7885 - 0.7825 = +0.006

Gain = 0.004

Profit = (12,500,000)(0.004)/100

= $ 500


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INTEREST RATE FUTURES

Underlying asset : Debt instrument

Used to hedge interest rate risk

Also available for speculationFutures Price = 100 - % yield

= 100 - % interest

Futures price increases when interest rate falls.

To protect against fall in interest rate, buy futures

Applies when we have cash surplus


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Futures Price falls when interest rate increases

To protect against rise in interest rates, sell futuresApplies when we have a cash deficit situation

Futures contract value not directly givenHas to be calculated

Discount yield = 8.32%

Let T Bill Price = P(1,000,000 - P)/(1,000,000) X (360/90)X(100) = 8.32

P = 979,200


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Problem

December Eurodollar futures are trading at

89.25. A speculator believes interest rates are

going to rise. What should he do ? If on the

date of settlement, futures quote 88.75, what

is his gain or loss?


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Solution

Sell futures

100-89.25 = (1,000,000- A)/(1,000,000)x400

A = $ 973,125

100-88.75= (1,000,000-B)/(1,000,000)x400

B = $ 971,875

Gain = A - B = 973,125 - 971,875

=1250


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Problem

On January 5, March futures maturing after 77 dayson March 22 are yielding 12.50%.

167 day T Bills are now yielding 10% while 77 day T

Bills are yielding 6%.

The yields given are actual and based on daily

compounding.

Are there any arbitrage possibilities ?


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Solution

Borrow for 77 days, Invest for 167 days, Sell March futuresAfter 77 days, collect money realised against sale of futures

Give delivery of T Bill and repay loan.

Price of 167 day T Bill = (1,000,000)/(1+.10)167/360 = $ 956,750Borrow $ 956,750 for 77 days.

After 77 days, realisation from sale of futures

= (1,000,000)/(1+.125)90/360 = $ 970,984

Repayment of loan

= (956,750)(1+.06)77/360 = $ 968,749

Profit = 970,984 - 968,749 = $ 2235


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Problem

Repeat previous problem if yield on 77 day T Bills is 8%.

Solution

Buy March futures. Borrow for 167 days. Invest for 77 days

In March, collect money from maturing 77 day T Bill. Pay and takedelivery against March futures. Hold till delivery.

To buy future we need 1,000,000/(1+.125)90/360 = $ 970,984

Investment today = 970,984/(1+0.08)77/360 = $ 955,131

Issue 167 day T Bill for $ 955,131

Buy 77 day T Bill for $ 955,131

Outflow after 167 days = (955,131)(1+.10)167/360= 988,308

Gain = 1,000,000 - 998,308 = $1,692


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OPTIONS - An Introduction

Right to buy / sell asset at pre specified price onor up to a specified date

Buyer has no obligation

Seller has obligation , charges Premium

Option buyer, Option seller / writer

Call & Put options

American & European Options

Strike price, Maturity Date


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OPTIONS - An Introduction

Intrinsic value implies Gain on immediateexercise

Option Value - Intrinsic Value = Time Value

At the money, In the money, Out of the moneyoptions


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Call Options

For buyer,

S E implies Profit = (S - E) - C

S: Spot Price, E: Exercise Price, C: Premium

For Option Seller / Writer,

S E implies Profit = -(S - E) + C


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Put Options

For Option buyer,

S E implies Profit = -P

For Option Seller,

S E implies Profit = P, where P - Premium


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Option Strategies

Bullish & Bearish Spread

Butterfly Spread

Straddle & Strangle


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Bearish spread

-5

-4

-3

-2

-1

0

1

2

3

4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Price

Profit

Series1


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Bullish spread

-6

-4

-2

0

2

4

6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Price

Profit

Profit


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Straddle

0

1

2

3

4

5

6

1 2 3 4 5 6 7 8 9 10 11 12

Price

Profit

Profit


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Range Forwards

Two prices, F1, F2 are agreed to at the beginningof the contract

Buyer can buy foreign currency at :-

F1 if Spot Price < F1F2 if Spot Price > F2

Spot Price if F1 < Spot Price < F2 , at the time of

maturity of the contract

No up front payment is involved


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Illustration - I

You want to write a call option on the dollar andexpect the spot prices at the date of maturity to

have the following probability profile.

Spot Price: 41 42 43 44

Probability: 0.20 0.30 0.30 0.20

If the strike price is 42.50 and you are writing a

naked call, what premium should you charge ?


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Solution - I

Let Premium charged be p. Then, the pay off canbe tabulated as

Spot Price Pay off Pay off * Probability

41 p 0.2 p42 p 0.3 p

43 p - 0.50 0.3 (p - 0.50)

44 p - 1.50 0.2 (p - 1.50)Total: p - 0.45

To break even, p - 0.45 = 0 or p = 0.45


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Illustration - II

In the earlier problem, assume you were writing anaked put option. All other details remain the

same. What premium should you charge ?


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Solution - II

Let Premium charged be p. Then, the pay off canbe tabulated as

Spot Price Pay off Pay off * Probability

41 p - 1.50 0.2 (p - 1.50)42 p - 0.50 0.3 (p - 0.50)

43 p 0.3 p

44 p 0.2 pTotal: p - 0.45

To break even, p - 0.45 = 0 or p = 0.45


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Illustration - III

As an option writer, you are confident that theprice of the dollar can move only in the range 34

- 39 at maturity. At present, the dollar is trading

at 36. Assume it is an European Call option witha strike price of 36 and you plan to cover the call

by going long in dollars, work out the following:-

a) Number of dollars which must be purchased per

option written.

b) Option premium, ignoring interest costs.


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Solution - III

Buy x dollars per option written.Investment today = 36 x - p

Returns at the time of maturity of option

S = 34 Option not exercised, Returns = 34 xS = 39 Option exercised, Returns = 39 x - 3

Riskless portfolio 34 x = 39 x - 3 = 36 x - p

x = 0.6

Also, (34)(0.6) = (36)(0.6) - p p = 1.2

Premium = Rs. 1.2/$


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Illustration - IV

The following Call Options are trading

Strike Price Premium

30 3

35 1

Explain how you can use a spread strategy to limit

both upside and downside risk.


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Solution - IV (Alt I)

Buy option with Strike Price = 30 &

Sell option with Strike Price = 35.

S


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Spread Strategy

-3

-2

-1

0

1

2

3

4

0 10 20 30 32 35 40 45 50

X

Y


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Solution - IV (Alt II)

Suppose we Sell option with Strike Price = 30 &

Buy option with Strike Price = 35.

S


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Spread Strategy

-4

-3

-2

-1

0

1

2

3

0 10 20 30 32 35 40 45 50

X

Y


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Illustration - V

The following Call Options are trading

Strike Price Premium

A 55 8

B 60 5

C 65 3

You are confident that the Spot Price will be close

to 60 but would like to cover risk in case ofunexpected volatility. Suggest a Spread Strategy.


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Solution - V (Alt I)

Buy A, C and Sell 2 B

S


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Spread Strategy

-2

-1

0

1

2

3

4

5

55 56 60 64 65

X

Y


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Solution - V (Alt II)

Sell A, C and Buy 2 B

S


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Spread Strategy

-5

-4

-3

-2

-1

0

1

2

55 56 60 64 65

X

Y


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INTEREST RATE FUTURES

Underlying asset : Debt instrument

Used to hedge interest rate risk

Also available for speculationFutures Price = 100 - % yield

= 100 - % interest

Futures price increases when interest rate falls.To protect against fall in interest rate, buy futures

Applies when we have cash surplus


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Futures Price falls when interest rate increases

To protect against rise in interest rates, sell futuresApplies when we have a cash deficit situation

Futures contract value not directly givenHas to be calculated

Discount yield = 8.32%

Let T Bill Price = P

(1,000,000 - P)/(1,000,000) X (360/90)X(100) = 8.32

P = 979,200

P bl


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Problem

December Eurodollar futures are trading at

89.25. A speculator believes interest rates are

going to rise. What should he do ? If on the

date of settlement, futures quote 88.75, what

is his gain or loss?

S l ti


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Solution

Sell futures

100-89.25 = (1,000,000- A)/(1,000,000)x400

A = $ 973,125

100-88.75= (1,000,000-B)/(1,000,000)x400

B = $ 971,875

Gain = A - B = 973,125 - 971,875

=1250

P bl


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Problem

On January 5, March futures maturing after 77 days

on March 22 are yielding 12.50%.

167 day T Bills are now yielding 10% while 77 day T

Bills are yielding 6%.

The yields given are actual and based on daily

compounding.

Are there any arbitrage possibilities ?

S l ti


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Solution

Borrow for 77 days, Invest for 167 days, Sell March futures

After 77 days, collect money realised against sale of futures

Give delivery of T Bill and repay loan.

Price of 167 day T Bill = (1,000,000)/(1+.10)167/360

= $ 956,750Borrow $ 956,750 for 77 days.

After 77 days, realisation from sale of futures

= (1,000,000)/(1+.125)90/360 = $ 970,984

Repayment of loan

= (956,750)(1+.06)77/360 = $ 968,749

Profit = 970,984 - 968,749 = $ 2235

P bl


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Problem

Repeat previous problem if yield on 77 day T Bills is 8%.

Solution

Buy March futures. Borrow for 167 days. Invest for 77 days

In March, collect money from maturing 77 day T Bill. Pay and takedelivery against March futures. Hold till delivery.

To buy future we need 1,000,000/(1+.125)90/360 = $ 970,984

Investment today = 970,984/(1+0.08)77/360 = $ 955,131

Issue 167 day T Bill for $ 955,131Buy 77 day T Bill for $ 955,131

Outflow after 167 days = (955,131)(1+.10)167/360= 988,308

Gain = 1,000,000 - 998,308 = $1,692


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Thank You

futures and options- a primer

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