1. Options
Chapter 16

2. Overview The option concept is quite simple.
Instead of buying stock shares today, you buy an option to buy the stock at a later date at a price specified in the option contract.
You are not obligated to exercise the option.
But, if doing so benefits you, of course you will.
Moreover – the most you can lose is the original option price, which is normally only a fraction of the stock price.

3. History
Options have been around almost as long as common stock, but were not terribly popular until 1973.
The Chicago Board Options Exchange (CBOE) was established, and since, options trading has had tremendous growth.
Much of the success is due to the flexibility of options:
Speculative investors can use them to increase returns.
Careful investors can use them to reduce risk.

4. Review Options are derivative securities. Call options Put options
Value is ‘derived’ from some other underlying asset
Call options
Grants holder the right (not the obligation) to buy an underlying security at a given strike price before the option expiration date.
Put options
Grants holder the right (not the obligation) to sell an underlying security at a given strike price before the option expiration date.

5. Options are contracts
All contracts need ‘terms’. Options contracts must stipulate (at least) the following terms:
The identity of the underlying stock
The strike price (exercise price)
The option contract size
The option expiration date (option maturity)
The option exercise style
American or European
The delivery or settlement procedure
Standard delivery is within 2 business days after the exercise

6. Call option example
Assume that the buyer of a call option paid $2 for the right to buy a firm’s stock for $100 in three weeks. Further assume:
At the end of three weeks, the stock is trading at $110.
The option buyer will execute the call option. The buyer is able to buy the stock for $100 (using the call option) and then sell the stock on the market for $110.
At the end of three weeks, the stock is trading at $90. 
The call option will expire worthless. There is no reason to buy the stock for the option’s strike price of $100 when it can be purchased on the market for $90.
At the end of three weeks, the stock is trading at $100.
The call option will expire worthless. There is no reason to buy the stock for the option’s strike price of $100 when it can be purchased on the market for $100.

7. Put option example
Assume the buyer purchased a put option, paying a premium of $2 for the right to sell the firm’s stock for $100 in three weeks. Further assume:
At the end of three weeks, the stock is trading at $110.
The put option will expire worthless. There is no reason to sell the stock for the option’s strike price of $100 when it can be sold on the market for $110.
At the end of three weeks, the stock is trading at $90. 
The option buyer will execute the put option. The buyer is able to buy the stock at $90 on the market and then execute the option to sell it at $100.
At the end of three weeks, the stock is trading at $100.
The put option will expire worthless. There is no reason to sell the stock for the option’s strike price of $100 when it can be sold on the market for $100.

8. Options provide leverage
What would be the (3-week) percentage returns of an investor who chooses to buy a $100 stock outright (go long) vs. an investor who instead chooses to purchase a $2 call option on a $100 stock (expiring in 3 weeks)? Assume the following scenarios:
At the end of three weeks, the stock is trading at $110.
Option buyer 
The option buyer “invested” $2
The option buyer will enjoy a gain of $8 ($10 gain - $2 premium = $8)
Option percentage return = $8 / $2 = 400%
Stock buyer (long investor)
The long investor will invest $100 buying the stock
The long investor will enjoy a gain of $10
Long percentage return = $10 / $100 = 10%

9. Leverage works negatively as well
At the end of three weeks, the stock is trading at $90.
Option buyer
The option buyer “invested” $2 which expires worthless
Option percentage return = - $2 / $2 = - 100% return
Stock buyer (long investor)
The long investor will invest $100 buying the stock and lose $10
Long percentage return = - $10 / $100 = - 10%

10. Option “Moneyness” In-the-money options Out-of-the-money options
One that would yield a positive payoff if exercised immediately
Out-of-the-money options
One that would NOT yield a positive payoff if exercised.

11. Options chain example

12. Option exercise style
Options can either have an American or European exercise style.
American options can be exercised anytime up until maturity.  
All listed stocks
All listed ETFs
European options can only be exercised at expiration.
Most stock indices (with the exception of S&P 100)

13. Stock index options
After stock options were such a big hit, the exchange started looking for other financial products to utilize options. In 1982, the CBOE created stock index options:
S&P 100 (OEX) – American style
S&P 500 (SPX) – European style
Dow (DJX) – European style
Settlement is a little different for stock index options (imagine trying to settle with the actual underlying securities).
Cash-settled options

14. Option writing Thus far, we have discussed only “buying” options.
Selling (or ‘writing’) options is also an investment strategy.
Option writing involves receiving the option price and, in exchange, assuming the obligation to satisfy the buyer’s exercise rights (if needed).
A call writer is obligated to sell stock at the option’s strike price if the buyer exercises the call option.
A put writer is obligated to buy stock at the option’s strike price if the buyer exercises the put option.

15. Option payoffs
It is easier to think about option investment strategies in terms of:
Initial cash flows – the option price (premium)
For the buyer, this is outflow
For the seller, this is inflow
Terminal cash flows – the option’s payoff realized from exercising the option
For the buyer, this is inflow
For the seller, this is outflow

16. Call option payoffs

17. Put option payoffs

18. Using options to manage risk
Thus far, we have looked at the payoffs and profits from buying and writing individual calls and puts.
What happens when we start to combine puts, calls, and shares of stock.
There are numerous combinations, but we will stick to just a few of the most basic and important strategies.

19. Covered calls
Suppose you own a share of Alcoa (AA) stock, currently worth $45. Suppose you also write a call option with a strike price of $45 for $3. What is the net effect?
If AA stays below $45, the buyer’s call option will expire worthless and you would pocket the $3.
If AA rises above $45, the buyer will exercise the call, and you must deliver the stock at $45.
Thus, when you sell a call option on stock you already own, you keep the option premium no matter what. The worst thing that can happen is that you have to sell at $45
Because you already own the stock, this is called a covered call strategy.

20. Covered vs. naked calls
Covered calls exchange future “upside” potential for certain cash today, thereby reducing risk and potential reward.
In contrast, selling call options on stock you do not own is known as a “naked” call strategy and has UNLIMITED LOSS POTENTIAL.
Thus – selling calls is either highly risky or else acts to significantly reduce risk – depending on whether or not you own the underlying asset.

21. Protective puts
Suppose you own a share of Alcoa (AA). stock, currently worth $45. Suppose you also purchase a put option with a strike price of $45 for $2. What is the net effect?
If AA stays above $45, your put will expire worthless and you would lose $2.
If AA falls below $45, you would exercise your put, and the put writer would pay you $45 for the stock. No matter how far it falls – you will receive $45.
Thus, by purchasing a put option, you have protected yourself against a price decline. You have paid $2 to eliminate your downside risk.
Buying a put option on stock you already own is called a protective put strategy. It’s like buying insurance.

22. Spreads
A spread strategy involves taking a position on two or more options of the same type.
Bull call spreads – buy a call and also sell a call with a higher strike price. Betting value increases.
Example: Assume you buy $11.50 BAC call for $430 and sell $12 BAC call for $400. You are currently out-of-pocket $30.
If BAC goes higher, you exercise the $11.50 call option to buy at $1,150 and sell (cover) for $1,200, earning $50.
Your profit = $50 - $30 = $20
For more – check out
Center

23. Bull call spread

24. Other spreads There are also:
Bear call spreads – buy a call and also sell a call with a lower strike price. Betting value decreases.
Butterfly spreads – Use call options with equally spaced strikes, buy one call with the lowest strike and buy one call with the highest strike while also selling two options with the middle strike. Betting value doesn’t move much.
For more – check out
Center

25. Bear call & Butterfly

26. Combinations
A combination strategy mixes call and put options. The best known is the straddle.
Suppose a share of stock is worth $50. You think something major is going to happen, but you don’t know if it will be good or bad. What could you do?
One answer is to buy a call and buy a put, both with a $50 exercise price (long straddle).

27. Long straddle

28. Other combinations

29. Warning about options
Options may have to move 10-15% or more in a short time period before an investor recovers the price & commission.
Options are by definition short-term instruments; an investor can ride out bad times in spot markets but not in options.
The limited loss feature makes options appear safer than they are.
You have to compare equal $ investments in stocks and options to really see the higher risk of the option position.
Options are traded in a highly competitive market.

30. Option valuation basics
While option valuation can become extremely complex, at the most fundamental level, an option’s value is derived from two simple components – the option’s intrinsic value and the premium for the option’s time value.

31. Intrinsic value example
Assume a stock has a market price of $63. It could be quickly surmised that a call option with a strike price of $60 has an intrinsic value of $3 while a call option with a strike price of $55 has an intrinsic value of $8.

32. Time premium example
Assume it is currently February 10th and you are researching a call option for Under Armor (UA) which is currently trading for $75.45 per share. You first look at a call option expiring on February 19th with a strike price of $ The premium is $2.90.
This option has an intrinsic value of 95₵ since the strike price of $74.50 is currently below the market price of $ This means that the option’s time premium is ( ) = $1.95

33. The Black-Scholes option pricing model
The Black-Scholes model extends upon the logic that an option’s price is based on its intrinsic value and time premium. The model expands the number of variables to include:
The price of the stock
The option’s strike price
The time until expiration
The price volatility of the stock
The current risk-free rate

34. Summary of variable movement’s impact on option value

35. Estimating price volatility
One method to estimate the price volatility of your stock is to use the stock’s standard deviation. You can calculate the standard deviation by researching the historical prices of the stock and using them to find the expected return and variance.
Another popular and relatively easy method of estimating stock price volatility is to find an estimate of future volatility using an existing index. For instance, the S&P Volatility Index (VIX) is an estimate of investor expectations of stock market volatility, which are based on S&P 500 firm options.

36. Free on-line Black-Scholes calculators
Run a search for “free Black-Scholes option calculator” you will find several websites that provide free Black-Scholes valuations.
For instance, the Economic Research Institute provides a free Black-Sholes calculator at You simply input the following information and hit “calculate”:

37. Black-Scholes in practice
There are numerous reasons as to why performing the Black-Scholes model may provide you with unreasonable valuation estimates.
Perhaps the most limiting factor of the Black- Scholes model is that it calculates a value based on the European-style of option only (not the more popular American option).