Trading in Financial Markets
5.5 Plain Vanilla Derivatives
5.5.4 Options
The valuation of plain vanilla interest rate swaps is discussed in Appendix D at the end of this book.
and December 2017. The August options have an expiration date of August 18, 2017; the October options have an expiration date of October 20, 2017;
and the December options have an expiration date of December 15, 2017.7 Intel's stock price was $35.91
Table 5.6 Prices of Options on Intel, June 12, 2017 (stock price =
$35.91)
Strike Price ($) Calls Puts
Aug. 17 Oct. 17 Dec. 17 Aug. 17 Oct. 17 Dec. 17
34 2.48 2.88 3.15 0.63 1.07 1.42
35 1.77 2.23 2.53 0.95 1.41 1.80
36 1.18 1.66 1.98 1.39 1.85 2.25
37 0.74 1.20 1.22 1.98 2.40 2.79
Suppose an investor instructs a broker to buy one October call option contract on Intel with a strike price of $36. The broker will relay these instructions to a trader at the CBOE. This trader will then find another trader who wants to sell one October call contract on Intel with a strike price of $36, and a price will be agreed upon. We assume that the price is
$1.66, as indicated in Table 5.6. This is the price for an option to buy one share. In the United States, one stock option contract is a contract to buy or sell 100 shares. Therefore, the investor must arrange for $166 to be remitted to the exchange through the broker. The exchange will then arrange for this amount to be passed on to the party on the other side of the transaction.
In our example, the investor has obtained at a cost of $166 the right to buy 100 Intel shares for $36 each. The party on the other side of the transaction has received $120 and has agreed to sell 100 Intel shares for $36 per share if the investor chooses to exercise the option. If the price of Intel does not rise above $36 before October 20, 2017, the option is not exercised and the investor loses $166. But if the Intel share price does well and the option is exercised when it is $50, the investor is able to buy 100 shares at $36 per
share when they are worth $50 per share. This leads to a gain of $1,400, or
$1,234 when the initial cost of the options is taken into account.
If the investor is bearish on Intel, an alternative trade would be the purchase of one December put option contract with a strike price of $36. From Table 5.6, we see that this would cost 100 × $2.25 or $225. The investor would obtain at a cost of $225 the right to sell 100 Intel shares for $36 per share prior to December 15, 2017. If the Intel share price moves above $36 and stays above $36, the option is not exercised and the investor loses $225. But if the investor exercises when the stock price is $25, the investor makes a gain of $1,100 by buying 100 Intel shares at $25 and selling them for $36.
The net profit after the cost of the options is taken into account is $875.
The options trading on the CBOE are American. If we assume for simplicity that they are European so that they can be exercised only at maturity, the investor's profit as a function of the final stock price for the Intel options we have been considering is shown in Figure 5.4.
Figure 5.4 Net Profit from (a) Buying a Contract Consisting of 100 Intel October Call Options with a Strike Price of $36 and (b) Buying a Contract Consisting of 100 Intel December Put Options with a Strike Price of $36 There are four types of trades in options markets:
1. Buying a call 2. Selling a call 3. Buying a put 4. Selling a put
Buyers are referred to as having long positions; sellers are referred to as having short positions. Selling an option is also known as writing an option.
When a trader purchases options for cash, there are no margin requirements because there are no circumstances under which the trade becomes a
liability for the trader in the future. Options on stocks and stock indices that last longer than nine months can be bought on margin in the United States.
The initial and maintenance margin is 75% of the value of the option.
When options are sold (i.e., written), there are potential future liabilities and margin must be posted. When a call option on a stock has been written, the initial and maintenance margin in the United States is the greater of
1. 100% of the value of the option plus 20% of the underlying share price less the amount, if any, by which the option is out‐of‐the‐money.
2. 100% of the value of the option plus 10% of the share price.
When a put option is written, it is the greater of
1. 100% of the value of the option plus 20% of the underlying share price less the amount, if any, by which the option is out‐of‐the‐money.
2. 100% of the value of the option plus 10% of the exercise price.
These margin requirements may be reduced if the trader has other positions in the stock. For example, if the trader has a fully covered position (where the trader has sold call options on a certain number of shares and owns the same number of shares), there is no margin requirement on the short option position.
Options trade very actively in the over‐the‐counter market as well as on exchanges. The underlying assets include stocks, currencies, and stock indices. Indeed, the over‐the‐counter market for options is now larger than the exchange‐traded market. Whereas exchange‐traded options tend to be American, options trading in the over‐the‐counter market are frequently European. The advantage of the over‐the‐counter market is that maturity dates, strike prices, and contract sizes can be tailored to meet the precise needs of a client. They do not have to correspond to those specified by the
exchange. The sizes of option trades in the over‐the‐counter are usually much greater than those on exchanges.
Valuation formulas and numerical procedures for options on a variety of assets are in Appendices E and F at the end of this book.