Topic 3 & 4 – Option contracts & trading strategies
Introduction
Option contracts can be traded on exchanges or over the counter. They are derivative instruments:
• A Call option gives the buyer the right, but not the obligation to buy an underlying asset at a specified price.
• A Put option give the buyer the right, but not the obligation to sell an underlying asset at a specified price.
They can be on many different underlying assets: equities, commodities, bonds, currencies etc.
The buyer of the option pays a premium (the price of the option) to own the call or put. The seller receives a premium for giving the buyer or owner of the option the right to exercise their option.
Option contracts have exercise (strike) prices and maturity (expiry) that are agreed at the start of the deal.
4.1 Types of options
Options can be on individual equities, indices (e.g. S+P 500, FTSE100), on commodities, currencies, interest rates and bonds. They can also be on the futures markets of these assets. There are two main types:-
European options can be exercised only on expiry, whereas American options can be exercised anytime.
Example of an option on Oil futures contract:
Trade – buy a $50 call option on March 2020 Oil futures contract. This is a bullish trade because it benefits from the underlying price going up.
Current premium is $2 and underlying trades at $50. The cost is $2 for the right to own the underlying asset at $50 by expiry next March 2020. We can draw an expiry pay off profile chart for this position:
source: author
Other expiry pay-out profiles:
The call option is the same as in our Oil example and the put option is the opposite pay out because it makes money when the underlying falls in price. The buyer of a put owns the right to be short the market at the strike price K.
The full set of call and put options:
Source: author
Price of an option = Premium = Intrinsic value + Time value
Intrinsic value is the value if the option is exercised now, it is positive if the option is in the money.
Time value is the difference between the premium and the intrinsic value (rearranging the equation).
If there is time left to expiry, the option will have some time value. There is a probability that the underlying may trade through the strike price, thus giving the option value. This probability is greater the longer the remaining time to expiry and higher the volatility of the underlying.
Moneyness of options
For calls:
In the money (ITM): ST> K
At the money (ATM): ST= K
Out of the money (OTM): ST< K
For puts:
ITM: K > ST
ATM: K= ST
OTM: K< ST
The probability of ending up in the money is at the heart of option pricing:
Example of options pricing for calls and puts on underlying Mar’20 £/$ futures trading 1.23:
Source : author
The 1.20 call is priced at 0.0626. This premium is made up of 0.03 intrinsic value and 0.0326 of time value. The underlying is trading at 1.23, so the 1.20 call is in the money (ST> K) because it gives the owner the right to be long at 1.20.
Notice how the option premiums rise as the strikes go in the money (obviously in different directions for calls versus puts).
Question:
Apple (AAPL) closed at $258. These were the latest closes for the AAPL Dec 2019 options:
Calls Strike Puts
8.15 250 2.71
5.10 255 4.63
3.00 260 7.55
Which of the three strikes shown (250,255,260) are in the money calls? (if any) and how much intrinsic and time value do they have?
Answer:
250 call is ITM with $8 intrinsic and $3.15 time value
255 call is ITM with $3 intrinsic and $2.10 time value
260 call is OTM
————END OF TOPIC FOR WEEK 3———————-to be continued [I will cover this material again and more below in week 4 recorded stream casts]
4.2 Option positions & strategies
Option strategies are a way of expressing market views. There is direction of the underlying: Bullish or bearish, or unchanged? There is volatility of the underlying: higher, lower or unchanged? When volatility increases the value of the options increase (both calls and puts).
Options are flexible tools to trade with because you can profit from many different market environments.
Source: CME options strategy guide
Different market environments for different strategies using options:
– Rising volatility and rising underlying market (bullish direction) = long call (top left box)
– Rising volatility and falling market (bearish) = long put
– Rising volatility and undecided direction = long straddle (buy call and put at same strike)
– Falling volatility and bullish direction = short put
– Falling volatility and bearish direction = short call
– Falling volatility and undecided direction = short straddle (sell call and put at same strike)
– Undecided volatility and bullish direction = bull spread (buy call and sell a higher call)
– Undecided volatility and bearish direction = bear spread (buy put and sell a lower put)
Example of a bull (or call) spread:
Market price is 100
• Buy call at 100
• Sell call at 110
• Moderately bullish, maximum profit at 110 expiry and stays constant above 110
• Max pay-out is 10, losses limited below 100 to net premium paid
source : author
Positions in an option and the underlying:
4.3 Stock options: protective puts, covered calls
Source: Figure 12.1 Hull: p 279
• Covered call – long the stock, short a call option
• Reverse of writing a covered call – short stock, long a call
• Protective put – long the stock, long a put
• Reverse of protective put – short stock, short a put
Example of protective put
Suppose you own stock worth £30 and wish to hedge against a fall in value. Solution is to buy put with strike at £30. Say this option costs £2. Strategy payoff profile looks like this:-
Values come from creating a pay-off table:
source: author
Fund managers and investors can use protective puts to hedge the value of portfolios against falling markets.
Another strategy using options with a long position in the underlying is the covered call (see a) above). Selling a higher price call against your existing long position will enhance returns in a quiet market by receiving premium for the short option position. It has the effect of lowering the average cost of the position. If the underlying rallies above the strike price, your stock is ‘called away’ from you and you have to deliver your stock to the buyer of the option.
Exercise:
Long shares at 100
Short 110 call
Premium of call = 10
Create a payoff table and expiry chart
Answer to exercise:
underlying
80
90
100
110
120
130
Share price
-20
-10
0
10
20
30
Call
0
0
0
0
-10
-20
Premium
10
10
10
10
10
10
Covered call
-10
0
10
20
20
20
End of exercise – Source: Author
Neutral strategy – sell butterfly spread – buy 1 call at 95, sell 2 calls at 100, buy 1 call at 105
source: author
Strategy makes money on expiry between 95 and 105, and only loses net premium paid above 105 and below 95. This neutral strategy also is referred to as a short volatility trade. Generally speaking long volatility trades benefit from underlying movement and short vol trades benefit from quiet markets.
Options can be used as flexible tools in conjunction with the underlying to hedge or enhance returns. They can be used in combinations to take advantage of quiet markets, or volatile markets.
4.4 Definitions and Applications: the Greeks
There are 5 factors driving the premium of an option:
S Underlying
X Strike
T Time to maturity
R interest rates
2 Volatility of underlying
All these factors are readily observable except for the variance, which has to be estimated.
There are two ways of estimating 2
• First method uses historical data on the underlying’s price movements
• Second method of estimating is to use Black-Scholes equation in reverse.
When the factors of strike price, time to maturity, interest rates and level of underlying are plugged into the equation it leaves premium and volatility. If historical volatility is entered it gives a certain premium, if current option market prices are entered if gives a level of volatility implied by the level of the premium. So, all else being equal with the other three factors, as premiums go up, volatility must go up and vice versa.
Essential Greek definitions:
Each of these Greeks affect the price of an option, so each one has a different dimension of risk to the option position.
Option traders have to understand each to be able to manage risk effectively.
Dealing with delta:
Delta can be looked at in different ways:
• It is the relative change of the options price in relation to the underlying (sensitivity)
• It is the probability of exercise
• It is the tangent to the slope of the price of the option
• It is used to calculate how many units of the underlying are needed to hedge the exposure
Call deltas can go from 0 to 1, put deltas go from 0 to -1.
Why? As the underlying moves up from OTM to ITM the call option gains intrinsic value and is more sensitive (closer to 1 to1) to the underlying movements. The probability of exercise is higher when the option is ITM. The same is true for puts, but inverse so the negative sign.
Delta exposure
Here we can use the delta of options to delta hedge the exposure. Option traders want to know their exposure in the units of the underlying.
Example:
Suppose your position is long 10 call options (1 call = 100 shares) of Microsoft (MSFT)
If the option delta is 0.25, how many shares should you buy or sell to be delta hedged?
Answer:
Option delta: + 0.25
Delta exposure: + 250 shares (0.25*10*100)
Delta hedge: short 250 shares
Question:
If you are long 50 put options (1 put = 100 shares) on Apple (AAPL) with an option delta of 0.85, how many shares should you buy or sell to be delta neutral ?
Answer:
Option delta: – 0.85
Delta exposure: – 4250
Delta hedge: long 4 250 shares (-0.85*50*100 = -4250)
Readings: Chapter 19 – Hull p 424-430
Quiz
1. Which option strategy has the best profit potential if the underlying rallies sharply?
• Short straddle (short same strike call and put)
• Long put
• Short put
• Long call
2. If the option strategy is ‘sell a call’ – which of the following is NOT true?
• You think the market will do nothing
• You think volatility will rise
• You are bearish
• Certain that the market will not rise
3. As an ‘in the money’ call option approaches expiration it will approach a delta of:-
• 0
• 0.25
• 0.50
• 1
4. What are the components of the premium on an out-of-the-money put option?
• Intrinsic value + zero time value
• Zero intrinsic value + zero time value
• Zero intrinsic value + time value
• Depends on the level of volatility
5. If the 190 Tesco puts are trading at 20p and Tesco shares are trading at 215p, how much intrinsic and time value do the 190 puts have?
• 20p intrinsic and 5p time value
• 25p intrinsic and 0p time value
• 0p intrinsic and 20p time value
• Impossible to tell
6. You have bought ATM calls (delta 0.5) on 5000 Microsoft shares and sold 5000 of the underlying shares. What is your net delta exposure?
• Zero
• Long 2500 shares
• Short 2500 shares
• Short 5000 shares
7. ATM puts have deltas close to:
• 0.5
• -0.5
• 1
• -1
8. What is the maximum profit to be made from selling a call option?
A. Unlimited gains
B. The premium
C. The expiry price
D. Strike price plus premium
[ Answers below ..… don’t look yet, until you have tried them all]
Answers: 1D,2B,3D,4C,5C,6C,7B,8B