Post on 15-Jul-2015
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Options and Futures Markets
Class #3
26.3.2015
Prof Rafi Eldor
Mr. Eitan Zeevi
©All rights reserved to prof. Rafi Eldor
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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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Underlying price at expiration date
Breakeven
Option value at expiration date
Payoff/Profit
Payoff at expiration date
Put option payoff as a function of the underlying price at
expiration date (for the buyer)
Put Option Fundamentals
4.003.98
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Put option payoff as a function of the underlying price at
expiration date (for the buyer)
Put Option Fundamentals
USD/ILS Buy Put 4.00 Expiration 28.3.15
Cost -200
Strike Payout Profit
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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Underlying price at expiration date
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
Put Option Fundamentals
Option value at expiration date
Payoff at expiration date
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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)
Put Option Fundamentals
USD/ILS Sell Put 4.00 Expiration 28.3.15
Cost +200
Strike Payout Profit
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
Put Option Fundamentals
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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
Put Option Fundamentals
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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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Financial Alchemy With Options
Box Spread Strategy
Strategies: Bull Spread
Vanilla Strategies: Straddle, Strangle, Risk Reversal
Put Call Parity
Strategies
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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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Call Spread Strategy – Call Bull Spread
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
Bullish on the market and spread on the exercise strikes
Call Option Fundamentals
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Call Spread Strategy – Bull Spread
Payout/Profit
Underlying price at expiration date
Option value at expiration date
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 with
the same expiration date.
Call Option Fundamentals
4.00 4.10
Profit
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Call Spread Strategy – Bull Spread
Call Option Fundamentals
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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Put Spread Strategy – Put Bear Spread
Payout
Underlying price at expiry
Option value at expiration date
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.
Put Option Fundamentals
3.90 4.00
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Buy Put USD/ILS strike 4.00 and sell Put strike 3.90
Put Option Fundamentals
USD/ILS Sell Put 3.90 Buy Put 4.00
Cost 30 -130 -100
Strike Payout Payout Profit
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
Bear Spread - Payout
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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
Strike Payout Payout Profit
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
USD/ILS Buy Put 4.00 Buy Call 4.00
Cost -150 -450 -600
Strike Payout Payout Profit
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 losses 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
Underlying price at expiration date
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
Strike Payout Payout Profit
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 profits from a stable market
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Short Straddle
Combination of selling a Call option and selling
a Put option with the same strike
Payout
Underlying price at expiration date
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
Underlying price at expiry
Combination of buying a Call option and
buying a Put option with different strikes
4.203.80
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Long Strangle
USD/ILS Buy Put 3.80 Buy Call 4.20
Cost -20 -110 -130
Strike Payout Payout Profit
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
Underlying price at expiration day
Combination of selling a Call option and selling
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 a long position on a Call
option and short position on a Put option (or vice versa), both
options with the same expiration date 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 a 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 buying
only 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
Underlying price at expiration date
Long call USD/ILS strike 4.10 and short Put 3.90
4.103.90 4.00Spot
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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
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Put – Call Parity is a principle referring to the relationship between the
prices of European Call option and a Put option with the same strike,
expirations date and underlying asset.
If this relationship doesn’t exist => Arbitrage opportunity
We will compare to portfolios:
1. A portfolio comprising from a Call option and an amount of cash
equal to the present value of the option's strike price
2. A portfolio comprising from a Put option and the underlying asset
Both options have the same expiration date and strikes.
Put – Call Parity
Definition
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S + P = C + X
S = Spot Rate
X = Strike
C = Call Price
P = Put Price
One way to look at the above formula:
Buy Spot + Put (protection from downside) = Buy T-Bill + Call (upside)
We had created two portfolios with Identical payout
Put – Call Parity
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Put – Call Parity
Buy Share at $50 Buy Put
50
Downside
Protection
(Put Option)
Bank deposit
paying $50Buy Call
50
Downside
Protection
(Cash)
50
50
Upside
from the
Share
Upside
from the
Call
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Practical use of Put Call Parity in USD/ILS
Market
Buy (or sell) synthetic forward and Sell (buy)
spot
*Remember Underlying is Forward not Spot
Transaction cost
Exchange options are Non- delivery
Put – Call Parity
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A synthetic forward can be created using:
1. Long Call
2. Short Put
Spot
Profit
Synthetic Forward
Put – Call Parity