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
2
0
1
0
-5
20
15
10
5
0 -
5
-
5
-
5
5
1
5
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 price
The 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 Shekel
As 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 Strikes
The lower the strike is of a Put option the lower the premium is (less
protection)
TA 25 example
Graph below describes the payout for P(1500,May) = 600
As 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 Straddle
Buying a Call option and buying a Put option, both with the same
strike, expiration date and notional amount.
Selling a Straddle
Selling 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 = 4.06
2. 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

50
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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