Options and futures markets #1 #2

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©All rights reserved to prof. Rafi Eldor

Options and Futures Markets

Class #1 + #2

12-19.3.2015

Prof Rafi Eldor

Mr. Eitan Zeevi

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Introduction

Fundamentals of Options

Forwards and Futures

Properties of Options

Binomial Option Pricing Model

Black and Scholes Formula

Volatility

Options Strategies

Options Pricing Parameters

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Introduction

What is a Derivative?

A financial Instrument whose price is derived from the

value/price of an Underlying Asset

Derivatives are traded on Exchanges or Over the

Counter (OTC)

Examples of Derivatives:

Forwards

Futures

Options

Swaps

Set of payments or payoffs

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Introduction

What is an Underlying?

The underlying is the asset whose value serves as the

reference for the derivatives price

There are many types of Underlings out there, for

example:

Currencies

Equity Stocks

Interest Rate

Commodities

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Introduction

Derivatives markets in numbers

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Options

o 1973 – Options trading launches at CBOE

o 1973 - Black-Scholes-Merton publish their path

breaking papers (Models)

o 1997 – Merton and Scholes received Nobel Prize in

economics

o 1993 – Options trading launches at Tel Aviv Stock

Exchange

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Example:

Construction company offers the following option:

For an up front payment today of $5,000, the client can buy an apartment next

year for a price of $100,000 (in addition to the $5,000 already paid)

Call Option Fundamentals

Apartment Price in $ Payout Profit

70,000 0 -5,000

80,000 0 -5,000

90,000 0 -5,000

100,000 0 -5,000

110,000 10,000 5,000

120,000 20,000 15,000

130,000 30,000 25,000

140,000 40,000 35,000

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Price next year

20

10

-5

20

15

10

5

0 -5

-5

-5

5

15

80 12011010090

Option ValueOption Profit

0 0 0

Value/Profit

Example:

Construction company offers the following option:

For an up front payment today of $5,000, the client can buy an apartment next

year for a price of $100,000 (in addition to the $5,000 already paid)


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1. What is the break-even point?

2. Should we exercise the option in a year if Apt price is $102,000?

Value/Profit

Apartment

Price in a year time

-5

20

15

10

5

0

80 12011010090

Options ValueOptions Profit


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1. What is the break-even point?

2. Should we exercise the option in a year if Apt price is $102,000?

Answers:

1. Break-even point:

Strike + Premium = $100,000+ $5,000 = $105,000

2. Yes, the premium was already paid, since option payout is positive

the investor will exercise the option.

If the investor will not exercise the option => loss of $5,000 (premium)

If the investor will exercise the option => Profit from the option +$2000 minus $5,000 premium = Total of -$3,000


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Terminology Explanation

Underlying

asset

The underlying is the asset that must be delivered if

the contract is exercised

Strike priceThe strike price is the price at which the options holder

has the right to buy or sell the underlying asset

Expiration

Date

The last date on which the rights attached to an option

may be exercised

Premium The price of the option that the options holder pays

Call Option – Definition

The buyer of a Call option has the right to buy a predetermined amount of

the underling asset (notional) at a given price during specific period or at a

particular point in time against payment of premium


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Example

Graph below describes the payout for C(1500) = 1000 ShekelAs a function of TA25 at expiration date

Break-even at 1510

15501500

5000

1000-

TA 25 Index at expiration date

Value and Payoff


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Few Comments:

o Options value is always positive

o Value of the option at expiry is the difference between the

strike and the underlying price

o The profit is the value of the option at expiry minus the paid

premium

o The breakeven point is when profit from the options is zero,

for Call option it’s the Strike level + Premium

o The holder of the option should exercise the option if the value

of the option is positive at expiry time.


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Option on Tel Aviv 25 Index

European options with Cash Settled settlement

Underlying Tel Aviv 25 Index

(Underlying is multiplied by 100)

Strike As per the contract X 100

Expiry date Last Friday of the relevant month

Premium Market price as traded in the exchange


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Class #2

19.3.2015

Prof Rafi Eldor

Mr. Eitan Zeevi

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Call Option

The buyer of a Call option has the right (but not the

obligation) to buy a predetermined amount of the

underling asset (notional) at a given price during specific

period or at a particular point in time against payment of

premium


Break-Even Point

Option Value at expiration date.

Option Profit at expiration date

Profit/Value

Underlying Price at expiry.

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Selling a Call Option (writing an option)

Break-even

Payoff/Profit for the Seller

Underlying price at expiry

Option value at expiry

Payoff at expiry

Call option payoff as a function to the underlying price at

expiration date (for the seller)


4.00

4.0380

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Call option payoff and Profit as a function of the underlying price at

expiration date (for the buyer)

Sell Call USD/ILS strike 4.00 expiration date 30.4.15 = 380 ILS


USD/ILS Sell Call 4.00

Premium +380

Strike Payout Profit

3.70 0 380

3.80 0 380

3.90 0 380

4.00 0 380

4.10 -1,000 -620

4.20 -2,000 -1,620

4.30 -3,000 -2,620

4.40 -4,000 -3,620

Breakeven rate = 4.0000 + 0.0380 = 4.0380

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Profit/Loss Buyer Seller

Maximum Profit Unlimited Premium

Maximum Loss Premium Unlimited

Trading an option can also be considered as “zero

sum game”, for any dollar the buyer of the option

gains, the seller of the option losses the same

amount (and vice versa)


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Few Comments:

o Options value is always positive

o Value of the option at expiration date is the difference between

the strike and the underlying price

o The profit is the value of the option at expiry minus the paid

premium

o The breakeven point is when profit from the options is zero,

for Call option it’s the Strike level + Premium

o The holder of the option should exercise the option if the value

of the option is positive at expiration date.


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Exercise Type of an Option

o European – exercise is allowed only at the expiration date at a certain time

o American – exercise is allowed at any time till expiration date

o Bermudian – specific dates

o Asian – average of pre defined period (very common in Commodity options)

*Bermudian and Asian are Exotic options


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Settlement Arrangements

o Delivery – Physical delivery of the underlying asset

o Cash Settlement – the holder of the option receives the

difference between strike price and the underlying asset

price (Put option) or the difference between the

underlying asset price and the strike price (Call Option)


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Call Spread Strategy – Bull Spread

Payout/

Profit



Call spread strategy is a combination of two options, for example:Buying Call USD/ILS with strike 4.00 and selling Call USD/ILS with strike 4.10 for the

same expiration date.


4.00 4.10

Profit

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USD/ILS Call 4.00 Call 4.10

Cost -390 80 -310

Strike Payout Payout Profit

3.70 0 0 -310

3.80 0 0 -310

3.90 0 0 -310

4.00 0 0 -310

4.10 1,000 0 690

4.20 2,000 -1,000 690

4.30 3,000 -2,000 690

4.40 4,000 -3,000 690

Breakeven rate = 4.00+0.0310 = 4.0310

Buy Call USD/ILS 4.00 and sell Call USD/ILS 4.10

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Bull Spread strategy, scenarios:

o If market will move up – the buyer of the options will make a

profit (limited)

o If market will move down – limited loss

Example:

Buying Call options with Strike $50 (Premium $8) and sell Call

options with strike $55 (Premium $3)

For an investor who expects the price of the underlying

asset will go up


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Different exercise prices (Moneyness)

Moneyness:

In the money Strike is lower than current underlying rate

At the money Strike = Current underlying rate

Out of the money Strike is higher than current underlying rate

A call option value will be higher when option’s strike is lower

If your expectations are for a much higher underlying rate it is

recommended to buy Call options with higher strikes i.e. out of the money

options (cheaper options allow more leverage)


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Put Option

Definition:

The buyer of a Put option (long Put) has the right (but not the

obligation) to Sell a predetermined amount of the underling

asset (notional) at a given price during specific period or at a

particular point in time against payment of premium

Comments:o Option value can not be negative

o The value of the option at expiration date is the difference between the

strike and underlying rate.

Put Option Fundamentals

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Breakeven


Payoff/Profit

Payoff at expiry

Put option payoff as a function of the underlying price at



4.003.98

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Put option payoff as a function of the underlying price at



USD/ILS Buy Put 4.00 Expiration 28.3.15

Cost -200


3.70 3,000 2,800

3.80 2,000 1,800

3.90 1,000 800

4.00 0 -200

4.10 0 -200

4.20 0 -200

4.30 0 -200

4.40 0 -200

Breakeven rate = 4.0000 – 0.0200 = 3.9800

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600-1500

Payoff/Profit

Breakeven at 1494

Different StrikesThe lower the strike is of a Put option the lower the premium is (less

protection)

TA 25 exampleGraph below describes the payout for P(1500,May) = 600As a function of TA25 index at expiration date


Payoff at expiry


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Payoff at expiry

Selling a Put Option:

Put option payoff as a function of the underlying price at expiration date (for

the seller)

Payoff/Profit for the

seller


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Selling a Put Option:

Put option payout and profit as a function of the underlying price at

expiration date (for the seller)


USD/ILS Sell Put 4.00 Expiration 28.3.15

Cost +200


3.70 -3,000 -2,800

3.80 -2,000 -1,800

3.90 -1,000 -800

4.00 0 +200

4.10 0 +200

4.20 0 +200

4.30 0 +200

4.40 0 +200

Breakeven rate = 4.0000 – 0.200 = 3.9800

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Profit/Loss Buyer Seller

Maximum Profit Strike price minus premium

Premium

Maximum Loss Premium Strike price minus premium


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Moneyness for Put Option:

In the money Strike is higher than current underlying rate

At the money Strike = Current underlying rate

Out of the money Strike is Lower than current underlying rate


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Put Spread Strategy – Bear Spread

Payout



Put spread strategy is a combination of two Put options,

for example:Buying Put USD/ILS with strike 4.00 and selling Put USD/ILS with strike 3.90 for

the same expiration date.


3.90 4.00

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Bear Spread

Buy Put USD/ILS strike 4.00 and sell Put strike 3.90


USD/ILS Sell Put 3.90 Buy Put 4.00

Cost 30 -130 -100


3.70 -2,000 3,000 900

3.80 -1,000 2,000 900

3.90 0 1,000 900

4.00 0 0 -100

4.10 0 0 -100

4.20 0 0 -100

4.30 0 0 -100

4.40 0 0 -100

Breakeven rate = 4.0000 – 0.0100 = 3.9900

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Spot

Profit

Spot

Profit

Long

Call

Short

Call

Spot

Profit

Spot

Profit

Long

Put

Short

Put

Call and Put Payoffs

Summary

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Strategies

There are few types of Strategies

o Naked – buying or selling options without holding the underlying or

any other option to hedge this positon

o Hedging – buying/selling options as well as holding the underlying

o Spreads - combination of options, buy and sell

o Bull/Bear - Same expiration date – Different Strikes

o Calendar spread - different expiation dates –

Same/Different Strikes

Strategies

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Straddle

A straddle is a vanilla strategy, it can be either of the following:

Buying a StraddleBuying a Call option and buying a Put option, both with the same

strike, expiration date and notional amount.

Selling a StraddleSelling a Call option and selling a Put option, both with the same

strike, expiration date and notional amount.

Strategies

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Straddle

Long Straddle

Buying a Straddle (Long Straddle)

For an investor who wants to profit from a volatile market

Buy a Call option and a Put option with the same strikes,

same notional amount and for the same expiration date

For example: an investor will buy Call option with strike

$50 (premium $5) and a Put option with strike of $50

(premium $3), expiration date in 1 year.

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Long Straddle

Combination of buying a Call option and buying a Put option

with the same strike

Table of a long straddle: Long Call and Put strike 4.00, expiration date 28.3.2015

USD/ILS Buy Put 4.00 Buy Call 4.00

Cost -150 -450 -600


3.70 3,000 0 2,400

3.80 2,000 0 1,400

3.90 1,000 0 400

4.00 0 0 -600

4.10 0 1,000 400

4.20 0 2,000 1,400

4.30 0 3,000 2,400

4.40 0 4,000 3,400

4.50 0 5,000 4,400

* Investor is making a profit from sharp movements

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Long Straddle

If we look between 3.90 to 4.08


Cost -150 -450 -600


3.90 1000 0 400

3.92 800 0 200

3.94 600 0 0

3.96 400 0 -200

3.98 200 0 -400

4.0 0 0 -600

4.02 0 200 -400

4.04 0 400 -200

4.06 0 600 0

4.08 0 800 200

Maximum Loss

* Investor will loss if market is stable

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Long Straddle

Combination of buying a Call option and buying

a Put option with the same strikes Graph of a long straddle:

Payout/

Profit


We need to calculate 2 breakeven rates:

1. 4.00+0.06 = 4.062. 4.00 -0.06 = 3.94

4.063.94

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Straddle

Selling a Straddle (Short Straddle)

For an investor who wants to profit from a stable market

Sell a Call option and a Put option with the same strikes,

same notional and for the same expiration date

For example: an investor will sell Call option with strike

$50 (premium $5) and a Put option with strike of $50

(premium $3)

Short Straddle

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Short Straddle

Combination of selling a Call option and selling

a Put option with the same strike

USD/ILS Sell Put 4.00 Sell Call 4.00

Cost 150 450 600


3.90 -1000 0 -400

3.92 -800 0 -200

3.94 -600 0 0

3.96 -400 0 200

3.98 -200 0 400

4.0 0 0 600

4.02 0 -200 400

4.04 0 -400 200

4.06 0 -600 0

4.08 0 -800 -200

Maximum Profit

* Investor will profit from a stable market

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Short Straddle


a Put option with the same strike

Payout


600

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Strangle

Strangle

A strangle is a vanilla strategy. It can be either of the following:

Long Strangle

Buying the Strangle. This involves buying a call option and

buying a put option, both with different strikes but with the same

expiration date and notional amount.

Short Strangle

Selling the strangle. This involves selling a call option and

selling a put option, both with different strikes but with the same

expiry date and notional.

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Strangle

Strangle

Why buy a strangle?

Like the straddle, the long strangle position expresses a view

that the prices will move (in which direction is irrelevant).

However, because the price needs to move further than with a

straddle the strangle is cheaper.

Strangles are commonly described as 25 delta, 15 delta and so

on, volatility quotes for strangles are used as benchmarks to

create a volatility surface (we will discuss that later in the

course).

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Long Strangle

Payout


Combination of buying a Call option and buying

a Put option with different strikes

4.203.80

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Long Strangle


Cost -20 -110 -130


3.70 1,000 0 870

3.80 0 0 -130

3.90 0 0 -130

4.00 0 0 -130

4.10 0 0 -130

4.20 0 0 -130

4.30 0 1,000 870

4.40 0 2,000 1,870

4.50 0 3,000 2,870

Table of a long strangle: Long Put 3.80 and Call 4.20, expiration date 28.3.2015

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Short Strangle

Payout



a Put option with different strikes

4.203.80

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Risk Reversal

Risk Reversal

What is Risk Reversal?

A Vanilla Strategy combined from long position on a Call option

and short position on a Put option (or vice versa), both options

with the same expiration day and with the same notional amount

Long Risk Reversal - Buy Call and sell Put with different strikes

Short Risk Reversal – Sell Call and buy Put with different strikes

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Risk Reversal

Risk Reversal

Why use Risk Reversal?

Hedge – the buyer of the Risk Reversal can hedge himself from

a higher spot rate.

Lower cost – buying a Risk Reversal is cheaper than just buying

a Call option.

“Zero cost Risk Reversal” – very popular, being used mostly by

corporates, combination of two options with the same premium.

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Risk Reversal

Payout


Long call USD/ILS strike 4.10 and short Put 3.90

4.103.90

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Box Strategy

+P(4.10) , -C(4.10) , -P(4.00) , +C(4.00)

S

Payout

4.00 4.10

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Box Strategy

+P(4.10) , -C(4.10) , -P(4.00) , +C(4.00)

4.00 4.10

S

1000

Payout

Options and futures markets #1 #2

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Transcript of Options and futures markets #1 #2