Objectives
Introduce call and put options:
– Understand both long and short option positions.
– Understand the decision rules (when will and when won’t the option
be exercised?).
– Understand the payoff diagrams (both call and put; both long and
short).
You need a strong understanding of these basic concepts:
– To be able to use options to hedge risk (Lecture 5).
– To be able to use options to speculate (Lecture 6).
– To be able to form option trading strategies using combinations of
options (Lecture 6).
– To have good intuition for how options are priced (Lectures 8-11)
2
Types of options
There are two main types of options:
– Call option: the holder has a right to buy the underlying asset at the
exercise/strike price within a specified period.
– Put option: the holder has a right to sell the underlying asset at the
exercise/strike price within a specified period.
3
Options give the holder flexibility
Recall the definition of a forward contract:
– “A long (short) forward contract is an agreement to buy (sell) an
asset at a specified price on a specified future date.” There is a
legal obligation to purchase (sell) the underlying asset.
In contrast, with options, the holder has the right to trade under
the terms of the contract, but there is no obligation to do so.
There are clear advantages to this flexibility (for both hedging
and speculation).
As a consequence, the option holder must pay to enter an
option contract (the option premium/price/value).
– this is a major difference between options and futures/forwards. For
forwards and futures, there is no upfront cost to enter a position
(ignoring margin deposits).
4
Types of options
The specific features of options varies widely. It is useful to
loosely classify options as either vanilla or exotic, depending on
how complicated their features are.
Options
Vanilla
European call
European put
American call
American put
Exotic
Binary options
Barrier options
Asian options
and many more
5
Exercise features
European options can only be exercised on the expiry date.
That is, on the expiry date, the holder gets to decide whether or
not they exercise their right.
American options can be exercised at any time up to and
including the expiry date.
nb: the vast majority of options traded on stock exchanges are
American style. However, to build basic intuition, we begin by
only considering European options.
6
Long call option
Assume that it is March. We enter a long call option on ABC. It
has a $10 exercise price, is European style with September
expiry, and trades at a $1.28 option premium.
– the long call option gives us the right to purchase ABC shares at
the pre-determined exercise price of $10.
– the decision whether or not to exercise this right is made at the end
of September (i.e., it is a European call option).
– Since we went long, we must pay the $1.28 option premium now.
To illustrate how a long call option works, consider two possible
prices for ABC shares at the end of September.
7
exercise or
“strike” price Option premium
or price or value
Long call option
Assume that, at expiry time T, ABC share price (ST) is $12.
– The long call gives us the right to purchase ABC shares for $10.
– Since the market price for ABC is $12, we will exercise this right to
buy ABC for $10.
– In effect, we buy shares under the long call for $10 and sell them
on market for $12, yielding a payoff of $2 per share.
– For a call option, ST > X is called in-the-money.
If, at expiry time T, ABC share price (ST) is $9:
– We can buy ABC shares under the long call for $10 if we want to …
– But they are only worth $9.
– We will choose not to exercise our right to buy and let the call
option lapse.
– For a call option, ST < X is called out-of-the-money. Decision rule for a call option: only exercise if ST > X 8
Gross payoff diagram: Long call
Gross
Payoff
X=$10 Share Price
0
Long Call Option
Gross Payoff = max[0, ST – X]
12
2
9
Net payoff diagram: Long call
Net
Payoff
X=10 Share Price
0 Option
Premium
-$1.28
12
$0.72
10
Breakeven point $11.28
(10 + 1.28)
Short call option – the counterparty
It’s quite easy to understand a call option from the perspective of
the long position:
– You pay the premium and get to make the decision whether or not
to exercise your right to buy.
Of course, there must always be a counterparty on the other
side of the transaction – the short call option (sometimes called
call option writer):
– As we will soon see, short option positions entail considerable risk.
– Therefore, the short position receives the option premium (as
compensation for the risk).
– The call option writer does not get to make a decision; rather, if the
long call holder chooses to exercise her right to buy, the option
writer is forced to sell the underlying share at the exercise price.
11
Short call option
Assume that it is March. We write (i.e., short) a call option on
ABC shares. It has a $10 exercise price, is European style with
September expiry, and trades at a $1.28 option premium.
– As the option writer, we receive the $1.28 call option premium.
While we don’t get to make the exercise decision, we certainly
know what decision rule the long call holder will use:
– the call will be exercised against us if ST > X.
– The long call will exercise their right to buy ABC shares for $10,
– And we (the short call) will be forced to sell ABC shares for $10.
12
Short call option
Assume that, at expiry time T, ABC share price (ST) is $12.
– The long call holder will exercise her right to purchase ABC shares
from us for $10.
– We will have to go into the market and buy ABC shares at $12,
– Then we are forced to sell them for $10, yielding a payoff of -$2 per
share.
If, at expiry time T, ABC share price (ST) is $9:
– The long call holder will not exercise; she will let the call lapse.
– That’s it – nothing further for us to do.
13
Gross payoff diagram: Short call
Gross
Payoff
Share Price
X = $10
0
Short Call Option
Gross Payoff = ‐̵ max[0, ST – X]
12
-2
Net payoff diagram: Short call
Net
Payoff
0 X = $10 Stock Price
Option
Premium
+$1.28
12
-0.72
15
Breakeven point $11.28
(10 + 1.28)
Long and short payoffs are symmetric
Payoff
X Share Price
Payoff
Share Price
X
Long Call
Short Call
16
Long put option
Assume that it is March. We enter a long put option on ABC. It
has a $10 exercise price, is European style with September
expiry, and trades at a $0.53 option premium.
– the long put option gives us the right to sell ABC shares at the predetermined
exercise price of $10.
– the decision whether or not to exercise this right is made at the end
of September (i.e., it is a European put option).
– Since we went long, we must pay the $0.53 option premium now.
To illustrate how a long put option works, consider two possible
prices for ABC shares at the end of September.
17
Long put option
Assume that, at expiry time T, ABC share price (ST) is $7.
– The long put gives us the right to sell ABC shares for $10.
– This is great – we can buy ABC on the market for $7, then sell them
to someone under the put option for $10, yielding a $3 payoff.
– For a put option, ST < X is called in-the-money. If, at expiry time T, ABC share price (ST) is $11: – We can sell ABC shares under the long put if we want to … – But this makes no sense since the market price for ABC is $11. – We will choose not to exercise our right to sell and let the put option lapse. – For a put option, ST > X is called out-of-the-money.
Decision rule for a put option: only exercise if ST < X 18 Gross payoff diagram: Long put Gross Payoff X = $10 Share Price 0 Long Put Option Gross Payoff = max[0, X – ST ] X 7 3 19 Net payoff diagram: Long put Net Payoff X=$10 Share Price 0 Option Premium -$0.53 7 $2.47 20 Breakeven point $9.47 (10 – 0.53) Short put option – the counterparty Long option positions are always easier to understand. As the holder of a long put option: – You pay the premium and get to make the decision whether or not to exercise your right to sell. the counterparty on the other side of the transaction is the short put option (sometimes called put option writer): – The short position receives the option premium (as compensation for the risk they are taking). – The put option writer does not get to make a decision; rather, if the long put holder chooses to exercise his right to sell, the option writer is forced to buy the underlying share at the exercise price. – This makes it risky for the put option writer. 21 Short put option Assume that it is March. We write (i.e., short) a put option on ABC shares. It has a $10 exercise price, is European style with September expiry, and trades at a $0.53 option premium. – As the option writer, we receive the $0.53 put option premium. We don’t get to make the decision, but we certainly know what decision rule the long put holder will use: – Put will be exercised against us if ST < X – We will be forced to buy ABC shares for $10 22 Short put option Assume that, at expiry time T, ABC share price (ST) is $7. – The long put holder will exercise his right to sell ABC shares for $10. – We are forced to buy those shares for $10. – When we dispose of them in the market, they are only worth $7 meaning we our payoff is -$3. If, at expiry time T, ABC share price (ST) is $11: – The long put holder will not exercise his right to sell. It is irrational to put shares on us for $10 when he can get $11 in the market! – The option will simply expire without ever being exercised against us. 23 Gross payoff diagram: Short put Gross Payoff Share Price X = $10 0 Short Put Option Gross Payoff = ‐̵ max[0, X – ST] -X 7 -3 24 Net payoff diagram: Short put Net Payoff X = $10 Share Price 0 Option Premium +$0.53 7 -2.47 25 Breakeven point $9.47 (10 – 0.53) Long and short payoffs are symmetric Payoff X Share Price Payoff Share Price X Long Put Short Put 26 X X X X Calls Puts Long Short 27 ASX option trading The Australian Securities Exchange (ASX) facilitates option trading on a variety of underlying assets: – About 90 large-cap stocks (https://www.asxoptions.com/directory.php) – Call and put options written on the S&P/ASX 200 market index – 3-year Treasury bonds Trading volume is respectable in some large caps and the S&P/ASX200, but very thin in many equities. In contrast, US exchanges facilitate trading on thousands of equities: – In 1973, the very first day options ever traded on CBOE, a mere 911 contracts exchanged hands spanning 16 stocks. – by 2014, about 1.3 billion option contracts were traded on 2,200 stocks, 22 indices and 140 ETFs. 28 ASX option trading For example, a wide range of call and put options trade on BHP. – BHP options expiring in Apr-20, May-20, Jun-20, Sep-20, Dec-20 and most other months. – For a given expiry, there is a range of exercise/strike prices. For other stocks, the range on offer is more limited (e.g., CBA, TLS, CSL, FLT, CCL, NAB, WOW, QAN). For the S&P/ASX 200 market index, there is an extensive range of expiry months and strike prices. These are index options. The asset underlying the option is the S&P/ASX200 market index. 29 30 31 Index closed at 5076 points Understanding the option tables (call option) Let’s zoom in on the BHP Apr-20 $28 call option: – This is an American call option. The holder can exercise their right to buy BHP shares for $28 at any time up until the expiry date. – On the ASX, the expiry date is (nearly) always the Thursday before the last Friday in the expiry month. So that would be Thursday 23rd Apr 2020. – This call has a strike price of $28 (a right to buy BHP for $28). Given that BHP share price is $28.98, this call is currently in the money. – The last trade of this call was for a premium (i.e., price) of $2.27. – Yesterday, there were 25 contracts for this call option traded. – Since this call first began trading, there have been 766 contracts opened that have not yet been exercised or closed out (this is the open interest). 32 ASX option trading Let’s imagine that we take a long position in the BHP Apr-20 $28 call: – In reality, we would go through a broker and would need to see the current price for this call. We would see bid/ask quotes which reflect one price for someone wanting a long position and a slightly different price for someone wanting a short position. – Anyway, let’s just assume that we can buy this call at $2.27. On the ASX, option contracts have a standard contract size covering 100 shares: – So we would pay a premium of $227 (100 shares $2.27). – We then have the right to buy 100 BHP shares for $28 each. 33 ASX option trading What happens next? – Any time between now and Thursday 23rd April, we can exercise our right to buy 100 BHP shares at the $28 strike price. – A long call position provides a payoff when share price rises above the strike price. This call is currently in the money, but we hope BHP share price rises much higher than $28.98. – We can easily calculate the breakeven point: given that we paid $2.27 for the long call and the strike price is $28, we need BHP share price to be above $30.27 for us to make a net profit. – If BHP share price finishes below $28 (OTM), we will let the option lapse and lose the $227 spent upfront. – If BHP finishes above $28 (ITM), we will exercise and receive a payoff. 34 BHP long call -2.27 Limited Loss Net Payoff Share price Strike price $28 Unlimited Potential Profit OTM ATM ITM Breakeven point = $30.27 (28 + 2.27) BHP short call Limited Profit +2.27 Strike price $28 Unlimited Potential Loss Breakeven point $30.27 Net payoff Share price Liquidating and closing out In many of our examples, I assume that the option is held until the expiry date, at which point we see if it is ITM or OTM, and make a (rational) exercise decision. Given that ASX options are American style, we don’t have to hold off until expiry. We can liquidate (or close out) our option position at any point. There are two ways to liquidate an option position: – Sell to close: options have value; they cost money to buy; they can also be sold. – Exercise: a long option position can always be liquidated by exercising (if it’s American-style). 37 Liquidating and closing out Assume that we already own the CSL Apr-20 $294 call. – Since current share price ($296.68) exceeds the strike price ($294), this call option is “in the money”. – We have until late Apr-2020 to exercise, but it is an American option and might decide to get out now. To liquidate this long call position, we could either: – “Sell to close”, in which case we receive the premium of $19.12, or – Exercise: this call is in the money (St > X). We could exercise our
right to buy CBA shares at $294, and immediately sell them at
market price of $296.68, realising a payoff of $2.68 per share
(ignoring transaction costs).
obviously, liquidating with a sell to close is optimal.
38
Understanding the option
tables (put option)
Let’s zoom in on the NAB May-20
$17 put option:
– This is an American put option. The holder
can exercise it at any time up until the
expiry date.
39
– The expiry date is (nearly) always the Thursday before the last Friday in
the expiry month. So that would be Thursday 28th May 2020.
– This put has a strike price of $17. Given that NAB share price is $16.68,
this put is currently in the money. A put needs share price below strike
price.
– The last trade of this put was for a premium (i.e., price) of $1.73.
– Yesterday, 10 contracts for this put option were traded.
– Since this put first began trading, there have been 45 contracts opened
that have not yet been exercised or closed out (open interest).
NAB long put
Limited Loss
-1.73
Breakeven point = $15.27
(17.00 – 1.73)
ITM OTM
ATM
Net
payoff
Share price
Strike price = $17
Short put option
Limited Profit
Breakeven point $15.27
Net
payoff
Strike price = $17
Share price
+1.73
Key takeaways from this lecture
Two basic options:
– Long call option: a right (but not obligation) to buy the underlying
asset at the strike price.
– Long put option: a right (but not obligation) to sell the underlying
asset at the strike price.
How to calculate the payoff to an option:
– Long call payoff = max [0,ST – X]
– Long put payoff = max [0, X – ST]
Shape of payoff diagrams for calls and puts:
– Both gross payoff and net payoff
– Both long and short positions.
– Calculate breakeven point 42
The post Introduction to option contracts appeared first on My Assignment Online.