1. Mechanics of Options Markets

2. The size of option market and importance of options
The size of option market size is far smaller than futures markets. However, as a nonlinear derivative product, its theoretical significance is far greater than other linear products.
All real investments are nonlinear. Initially one invest a lot, without any payoff. Later one invest very little, but with huge payoff.

3. Options
A call option is an option to buy a certain asset by a certain date for a certain price (the strike price)
A put is an option to sell a certain asset by a certain date for a certain price (the strike price) 12

4. Types of Options
A European option can be exercised only at the end of its life
An American option can be exercised at any time before the contract expires
There are many other types of options
Parisian option: Many convertible bonds are Parisian options
Asian options: Average price as strike price

5. Specification of Exchange-Traded Options
Expiration date
Strike price
European or American
Call or Put (option class)

6. Long Call on Microsoft
Profit from buying a European call option on Microsoft: option price = $5, strike price = $60 30 20 10 -5 40 50 60 70 80 90
Profit ($)
Terminal
stock price ($)

7. Short Call on Microsoft
Profit from writing a European call option on Microsoft: option price = $5, strike price = $60
-30
-20
-10 5 30 40 50 60 70 80 90
Profit ($)
Terminal
stock price ($)

8. Long Put on IBM
Profit from buying a European put option on IBM: option price = $7, strike price = $90 30 20 10 -7 90 80 70 60
100
110
120
Profit ($)
Terminal
stock price ($)

9. Short Put on IBM
Profit from writing a European put option on IBM: option price = $7, strike price = $90
-30
-20
-10 7 90 80 70 60
100
110
120
Profit ($)
Terminal
stock price ($)

10. Payoffs from Options What is the Option Position in Each Case?
K = Strike price, ST = Price of asset at maturity
Payoff ST K

11. Observation
The graph of the payoff structure of long call is identical to energy of electrons in photoelectric effect, a quantum effect.
The mathematical method we will use to find option prices is similar to methods in quantum mechanics.

12. Terminology Moneyness : At-the-money option In-the-money option
Out-of-the-money option

13. Terminology Intrinsic value Time value Example
Value realized if exercised immediately
Time value
Value over level of intrinsic value
Example
Spot price: 53; strike price: 50; Call option price: 5
Intrinsic value: 53 – 50 = 3
Time value: 5 – 3 = 2

14. Market Makers
Most exchanges use market makers to facilitate options trading
A market maker quotes both bid and ask prices when requested
The market maker does not know whether the individual requesting the quotes wants to buy or sell

15. Warrants
Warrants are options that are issued (or written) by a corporation or a financial institution
The number of warrants outstanding is determined by the size of the original issue and changes only when they are exercised or when they expire

16. Warrants (continued) Warrants are traded in the same way as stocks
The issuer settles up with the holder when a warrant is exercised
When call warrants are issued by a corporation on its own stock, exercise will lead to new stocks being issued

17. Executive Stock Options
Option issued by a company to executives
The purpose
When the option is exercised the company issues more stock
Usually at-the-money when issued
They cannot be sold
They often last for as long as 10 or 15 years

18. Executive Stock Options continued
What executives do when they are issued options?
Business Week, September 23, 2002 | Finance -- Stock repurchases can enrich execs at investors' expense
Execs may forfeit investing in projects with long term value so they have extra cash for repurchasing stocks, or the cash reserve becomes lower than it should be.
Discussion: Is there a perfect substitute?

19. Employee options
Startup or young companies often issue employee options.
If companies do well, early employees can become very wealthy. It is an very effective way to stimulate employees.
Bill Gates attributed the rapid growth of Microsoft in great part to its employee option program.
Do employee options have similar effect for large and mature companies?

20. Convertible Bonds
Convertible bonds are regular bonds that can be exchanged for equity at certain times in the future according to a predetermined exchange ratio

21. Convertible Bonds (continued)
Very often a convertible is callable
The call provision is a way in which the issuer can force conversion at a time earlier than the holder might otherwise choose
Amazon

22. Given that the value of an asset is affected by many factors and represented by relatively few financial instruments such as stocks and bonds, the financial market is far from complete. It is reasonable to expect that some derivative securities are created to better represent the values of the underlying assets. The convertible bond is an example.

23. For young and small firms not rated by a rating agency, it is difficult to issue straight bonds with low yield. At the same time, they may not want to issue additional shares at the current price level for this will dilute their ownership. Usually, small firms are volatile, which is often considered an unfavorable feature of a firm. However, the design of the convertible bond turns this feature into a positive one. The call options are highly valued since volatility is high for small firms. Because of the call option on the equity, convertible bonds pay lower coupon than the straight bonds. Since the convertible bonds properly “represent” the features of young and small firms, they have become increasingly popular among these firms, especially among high tech start-ups.

24. Price and volume of China Travel: Why trading volume is so high on some days?

25. Some background information
Parisian option. The option can be exercised only after the stock prices are over the strike price for a period of time. This feature is designed to prevent manipulation of share prices.
To force the conversion of the China Travel convertible bond into common shares, the daily closing price of China Travel stock had to stay over 5.49 HK dollars, the call price, which was 150% of the conversion price, for more than twenty of thirty consecutive trading days.

26. On August 6, 1997, the share price of China Travel went over the call price of HKD 5.49 for the first time. At that time, share prices of China Travel were higher than its CB prices, which is theoretically impossible. Figure shows the unusually high trading volume around that time, indicating strong market manipulation. However, the financial markets around Asia turned very bearish soon and China Travel managed to support its share price over the call price for nineteen days before it succumbed to the sharp fall of the general market.
For all its effort, China Travel could not convert the bond into equity.[1] The failure of conversion of China Travel gave a clear sign of the trend reversal. [2]

27. [1] According to the equity value of China Travel at the end of 1998, it would have made over sixty six million US dollar profit if the conversion had been successful, comparing with the total profit of seventeen million US dollar for the first half of the 1998.
[2] A trader confirmed that he spotted this signal and used it in trading. Several traders in different firms told me that borrowing shares of China Travel at that time was very difficult, although they didn’t understand why.

28. Homework 1
A trader buys a call option with a strike price of $45 and a put option with a strike price of $40. Both options have the same maturity. The call costs $3 and the put costs $4. Draw a diagram showing the variation of the trader’s profit with the asset price.

29. Homework 2
Two investors are bullish about gold. Each has one hundred thousand dollars to invest. Current price of gold is 1318 dollar per ounce. The first investor is a traditional one. She used all her money to buy gold. The second investor buys call options with the strike price at 1350 dollar per ounce. Suppose the option, which will mature in six months, costs 66 dollars for per ounce of gold. If gold price ends up at 1300 and1500 respectively after six months. What is the final wealth of each investor? What conclusion can you draw from the results? (For simplicity, we assume one can buy a fractional number of option contracts.)

30. Homework 3
Explain why an American option is always worth at least as much as a European Option on the same asset with the same strike price and exercise date.
Explain why an American option is always worth at least as much as its intrinsic value.

31. Homework 4
The asset values of companies A, B are both at 1000 million dollars. Each companies is purely financed with equity, with100 million shares outstanding. The stock prices of companies A, B are both at 10 dollars per share. Both companies provide their CEOs with shares or options as part of their packages. Company A provides its CEO 1 million shares. Company B provides its CEO call options on 10 million shares with strike price at 10 dollars and a maturity of 5 years. After five years, both companies’ asset value become 2000 million dollars. Please calculate the share price of company A and B, assuming share prices are accurate representation of asset value.