FMP 12: Options Markets
An option hands one side a right and leaves the other holding an obligation. A call option gives its buyer the right to buy an asset at an agreed price; a put option gives its buyer the right to sell one. Nothing compels the buyer to use that right, and the sum paid for holding it, at the moment the contract is struck, is the option premium.
Set that against a forward or a futures contract and the difference is sharp. Those bind both sides: whoever holds the long futures position must buy and whoever holds the short futures position must sell, at the agreed price, whatever has happened in between. No premium changes hands at the outset either, though futures traders post margin and forward counterparties may be asked for collateral. An option costs money at the start and can be abandoned at the end; a futures contract costs nothing at the start and cannot be abandoned at all.
Where options trade
Tens of millions of contracts change hands daily on United States exchanges: the CBOE, NASDAQ, the New York Stock Exchange, the International Securities Exchange. Abroad the venues include BM&FBOVESPA, the National Stock Exchange of India and the Eurex, and a large over-the-counter market sits alongside all of it.
A very long history
Bargains of this shape are ancient. Thales of Miletus, a Greek philosopher of over 2,500 years ago, reportedly paid for the use of olive presses at harvest and sold that right on at a sizable profit once the crop came in large. Dutch tulip wholesalers later bought calls to cap what bulbs would cost them and growers bought puts to protect the price they would receive, and when the mania collapsed in 1637 enough writers of puts defaulted to blacken the name of options across Europe. England went on to ban them for over 100 years. The nineteenth century financier Russell Sage, credited as the first to grasp put-call parity, dealt in both contracts on New York Stock Exchange stocks. Broker matching dominated, assisted by the Put and Call Brokers and Dealers Association, until the Chicago Board of Trade resolved in 1968 to build an options exchange. The Chicago Board Options Exchange opened five years afterwards with standardised calls and, more consequentially, the Options Clearing Corporation behind them demanding margin from sellers. Black-Scholes-Merton appeared in print that same year. Daily volume reached 20,000 call option contracts by 1974, and puts followed three years later.
Options divide on when the right may be used. A European call option or European put option may be exercised on one specific date only. An American call option or American put option may be exercised at any moment up to and including that date. That date is the expiration date, also called the maturity date, and the price at which the asset changes hands is the strike price, also called the exercise price. Geography has nothing to do with the naming: European contracts trade in Chicago and American ones in Frankfurt. The Bermudan option sits between them, exercisable on dates fixed in advance rather than continuously. Exchange-traded options are mostly American, while a great many written over-the-counter are European. Once, a new option was struck at whatever the asset was worth that day; now a range of strikes trades at once.
The distinction bears on valuation. Black-Scholes-Merton handles a European option, whereas an American option yields only to numerical procedures such as binomial trees. One simplification helps: certain American options ought never to be exercised ahead of maturity, and where that holds the American price and the European price coincide.
Moneyness
Moneyness places an option relative to the current price of the asset. Under the simplest definition, imagine exercising today, whether or not today is a permitted exercise date, and look at what comes out. Positive means in-the-money, negative out-of-the-money, zero at-the-money. Traders do use other definitions.
With the asset above the strike, the holder of a call option could buy below the going rate and sell straight back into the market, which is what puts that call in-the-money. Below the strike, the same logic favours the holder of a put option, who buys in the market and sells at the higher strike. Reverse either case and immediate exercise would not pay, so the option is out-of-the-money.
| Strike price | Call option | Payoff now | Put option | Payoff now |
|---|---|---|---|---|
| USD 50 | In-the-money | USD 5 | Out-of-the-money | USD 0 |
| USD 55 | At-the-money | USD 0 | At-the-money | USD 0 |
| USD 60 | Out-of-the-money | USD 0 | In-the-money | USD 5 |
Source: original illustration built on the chapter definitions. Payoffs are per share and ignore the premium.
Picture an asset worth USD 55 today. A European call option on it, struck at USD 60 and expiring in six months, is out-of-the-money and changes hands for a premium of USD 4. Write S for the asset price on the expiration date.
Anything below USD 60 leaves the long call position unexercised, since paying the strike for something the market sells more cheaply would be perverse. Above it the holder buys at USD 60 and sells on at once. Net of the premium, profit on exercise is S minus 60 minus 4, and a lapsed contract costs USD 4.
An awkward middle band follows, because exercise and a net loss can occur together, as they do for every S between USD 60 and USD 64. Declining to exercise there would still be wrong: abandoning the contract costs the whole USD 4, exercising less. At S equal to USD 61 the holder recovers USD 1 and finishes USD 3 down.
Whoever wrote the option, holding the short call position, sees the mirror image: the premium kept in full below USD 60, part of it retained between USD 60 and USD 64, and above USD 64 a loss that grows without limit as S rises. Options are zero-sum, so what one side gains the other loses to the penny.
Use that call option: strike USD 60, premium USD 4, six months to run.
Switch the contract. An asset stands at USD 62, and a European put option on it, struck at USD 60 with three months to run, is out-of-the-money and sells for USD 5. Again S denotes the asset price on the expiration date.
Below USD 60 the long put position is exercised: the holder buys for S in the market and delivers at the strike, so profit net of the premium is 60 minus 5 minus S. Above USD 60 the contract lapses and the loss is USD 5.
The awkward band reappears between USD 55 and USD 60, where exercise is worth doing and the trade still loses money, because the payoff recovers only part of the premium. For the writer everything inverts: the premium of USD 5 kept above USD 60, part of it kept between USD 55 and USD 60, and below USD 55 a loss bounded only by the asset falling to nothing, at which point the short put position has paid USD 60 for something worthless and is USD 55 down.
Use that put option: strike USD 60, premium USD 5, three months to run.
Profit diagrams fold the premium into the picture. A payoff diagram leaves it out and plots only what the contract is worth on the expiration date, given the asset price S and the strike price K. The payoff view is the one that composes cleanly when several options are combined into a strategy.
Four positions exhaust the possibilities, since a trader is either buying or selling and the contract is either a call option or a put option. Selling an option is also described as writing it.
Every payoff to a buyer is zero or positive, which is why a premium is charged at the outset, and every payoff to a writer is zero or negative, which is why the writer is paid.
Intrinsic value and time value
Payoff is a statement about expiration. Intrinsic value applies the same arithmetic to the asset price today, written as S sub zero, and measures what the option would be worth if exercise had to happen at once.
While time remains an option almost always trades above its intrinsic value, because the asset price can still move in the holder’s favour. That excess of premium over intrinsic value is the time value, and it drains away as expiry approaches until premium and payoff are the same number.
No exchange lists more options than the CBOE, which trades over a billion contracts each year. Its single-stock options are American-style, one contract covers 100 shares, and anything in-the-money at maturity is usually exercised automatically.
Expiration cycles
Every stock option belongs to one of three maturity cycles, the January cycle, the February cycle and the March cycle, spaced four months apart as the table shows. Four maturities trade at once: ahead of the third Friday of the current month they are the current month, the month after it, and the next two cycle months, and once that Friday passes the list rolls forward by one. Expiry lands on the third Friday, which made April 16, 2021 the maturity date of an April 2021 option. Trading runs every business day from 8:30 in the morning to 3:00 in the afternoon, Chicago time.
| Cycle | Cycle months | Trading after the third Friday of April |
|---|---|---|
| January cycle | January, April, July, October | May, June, July, October |
| February cycle | February, May, August, November | May, June, August, November |
| March cycle | March, June, September, December | May, June, September, December |
Source: cycle definitions from the chapter; the third column is derived from the rule above.
Two families sit outside that rhythm. Weeklys expire on Fridays other than the third, several of which are usually on offer, and LEAPS, or long-term equity anticipation securities, run out to three years and expire on the third Friday of January.
Strike price intervals
Strikes sit on a grid whose spacing widens as the underlying gets more expensive: multiples of USD 2.50 for a share priced between USD 5 and USD 25, usually multiples of USD 5 between USD 25 and USD 200, and usually multiples of USD 10 above USD 200.
A new contract carries only the three strikes nearest the current share price, with more added as the share moves. Open with the share at USD 19 and the middle strike is USD 20.00, flanked by USD 22.50 above and USD 17.50 below. Slip under USD 17.50 and a USD 15 strike appears; pass USD 22.50 and a USD 25 strike appears.
Strikes multiplied by maturities generate many contracts: five strikes on each of ten maturity dates could give 50 tradeable calls and 50 tradeable puts on one share. Every call on an underlying forms one class and every put another, while contracts inside a class sharing a maturity and a strike form an option series, so the IBM calls maturing in April 2021 are one series.
A stock on the March cycle trades at USD 41 when a new maturity is introduced.
Corporate actions shift a share price for reasons that say nothing about the fortunes of the business, and rules decide which of them force a change in option terms. Neutrality governs: neither the buyer nor the writer should end up better or worse off because a split or a dividend fell inside the life of the contract.
Cash dividends
An ordinary cash dividend leaves the terms alone. Exceptions arise only where a payment is unusually large, and the trigger is specific: a cash dividend exceeding 10% of the stock price sends the question to a committee formed by the Options Clearing Corporation. Early over-the-counter practice was different, cutting the strike by the dividend per share whenever one was declared.
Stock splits and stock dividends
A stock split does force an adjustment. Under a 5-to-1 split each share becomes five new ones, so the strike drops to a fifth of what it was while the trader’s contract count is multiplied by five. Any ratio works the same way.
Stock dividends run through the same machinery once restated as splits. A 10% stock dividend gives one new share for every ten held, which is arithmetically an 11-to-10 split, so the original strike is multiplied by ten-elevenths while the holding grows by 11/10.
An option has a strike price of USD 50. Three corporate actions are announced before it expires.
Single stocks are only part of what the exchange lists. Equity indices carry CBOE options too: the Russell 1000, the Dow Jones Industrial Average, the FTSE China 50, the FTSE 100, and both the S&P 500 Index and the S&P 100 Index. European-style exercise is common among them rather than American-style, and final settlement is in cash against the index value at a time fixed in advance. Index Weeklys mature on Wednesdays and Fridays, index LEAPS in December and June.
Options on exchange-traded products form another group. An exchange-traded fund may track an equity index, a bond index, a commodity or a currency, and the options written on it behave much like single-stock options: American-style, and settled physically by delivery of the underlying.
Non-standard products
Contracts breaking the standard mould are the exchange’s answer to over-the-counter competition. FLEX options allow non-standard strike prices, non-standard maturity dates and a choice between American and European exercise. Asian options and cliquet options on indices are listed as well: an Asian option pays off on the average price of the underlying across the life of the option instead of the price at one instant, while a cliquet option pays the sum of the monthly capped returns where that sum is positive. Not every innovation finds an audience. Credit event binary options, paying out if the underlying company defaulted before maturity, and deep-out-of-the-money put options, struck far below the initial price, both aimed at the credit derivatives market and both have been discontinued.
The over-the-counter options market
Away from the exchanges sits a substantial market of its own. Single-stock options trade mainly on exchange, but options on foreign currencies, interest rates and many other financial variables trade actively over-the-counter. The attraction is tailoring: a financial institution can shape strike prices, maturity dates and permitted exercise moments around one client. Deal sizes there are large, the contracts often run longer, and they can be exotic, departing from the plain call option and put option altogether.
Open outcry has given way to electronic matching across the options exchanges, but market makers have not gone anywhere. They stand ready to quote bid and ask prices on request, which is what keeps the market liquid, and the exchange caps the bid-ask spread so that the cost of demanding liquidity stays bounded. A trader wanting a position places an order through a broker, who charges a commission. Order types match those used in the futures market, the market order, the limit order and the stop order among them, and commissions differ from broker to broker, running as low as USD 5 per trade.
Closing out and open interest
Nobody is obliged to hold a position to expiry. Taking the offsetting trade closes it, so a trader owning a put option of a given strike price and maturity exits by selling a put option with that same strike price and maturity, and a writer exits by buying the identical contract back. Open interest counts the contracts still outstanding, exactly as in the futures market.
Position limits and exercise limits
How large any one participant can become is restricted. A position limit caps the contracts an investor may hold on one side of the market, and the sides are defined by direction rather than by contract type: long calls and short puts count together as one side, short calls and long puts as the other. An exercise limit caps how many contracts may be exercised inside five business days and is usually set at the same level. Both exist to stop one investor, or a group acting in concert, from pushing the market around.
Exercise and assignment
When the holder of a long option position exercises, somebody on the short side has to perform. A random procedure run by the Options Clearing Corporation picks that party from among the traders holding short positions, and whoever is picked is said to be assigned. Chance rather than queue position decides it, so a writer of many months standing carries the same exposure as one who wrote yesterday.
A stock in the United States can be bought partly on credit, with up to 50% of the price borrowed, which is what buying on margin means. Options are treated more strictly: one maturing in less than nine months must be paid for in full, while one maturing later can be bought on margin subject to a ceiling of 25% on the fraction borrowed. Anybody paying cash for an option owes nothing afterwards, so buyers post no margin. Writers stand elsewhere, since a written option carries a future liability that may turn out large.
| Written position | Base | Add-on candidate A | Add-on candidate B |
|---|---|---|---|
| Short call on a stock | 100% of sale proceeds | 20% of the share price, less however far the option sits out of the money | 10% of the share price |
| Short put on a stock | 100% of sale proceeds | As above | 10% of the strike price |
| Short option on an index | 100% of sale proceeds | 15% in place of the 20% | As for the stock rule |
Source: CBOE requirements from the chapter. Margin is the base plus whichever candidate is greater, and the rows are ordered so the one difference between the call and put rules stands out.
Cutting 20% to 15% for index options recognises that an index is normally less volatile than any single stock inside it. The sum is redone daily, with the option’s current market price standing in for the original proceeds, so a risen requirement calls for money to be added and a fallen one releases money.
Portfolios holding several option positions, sometimes alongside the underlying asset, fall under special rules in the CBOE Margin Manual. A covered call position, a written call option held together with the asset underlying it, attracts no margin, since the asset sits ready to be delivered.
Margin flows through the Options Clearing Corporation as it does through a futures clearing house. Every trade clears through an OCC member, so a non-member broker must arrange clearing with one that is. Brokers keep margin accounts with members and end users keep them with brokers, and no level may be less demanding than what the OCC asks of its members.
A trader writes four uncovered call option contracts of 100 shares each, taking a premium of USD 3 per share. The share trades at USD 48 against a strike of USD 55.
Three instruments carry option payoffs without being exchange-traded options, and one feature runs through all of them: exercising the right to obtain shares makes the company issue new stock. Trading an exchange-traded option merely expands or contracts the number outstanding.
Warrants
A warrant is an option issued by a corporation, usually a call option on its own stock, though it can be written on another asset such as gold. Warrants are frequently listed once issued, and exercise runs through the issuer rather than a clearing house: the holder contacts the company, fresh stock is issued, and the holder buys at the strike price. Firms also use warrants to sweeten a debt issue. A company whose stock stands at USD 40 might attach two warrants to each USD 1,000 bond, each carrying the right to buy one share at USD 45 on the expiration date, giving bondholders a stake in the upside rather than merely an interest in avoiding default.
Convertible bonds
A convertible bond, or convertible, works on similar lines: a bond exchangeable for equity at a ratio fixed when it is issued. Take a company whose share price is USD 40 issuing ten-year bonds of USD 1,000 par value, each convertible into 20 shares at any time after four years. Whoever converts receives newly issued stock. Convertibles, like warrants, often trade on exchanges.
Employee stock options
Employee stock options are call options a company grants to the people who work for it, and several features set them apart from anything listed on the CBOE. A vesting period, often as long as four years, must pass before exercise is possible, and employees leaving inside it may forfeit the options. Those leaving after vesting usually forfeit whatever is out-of-the-money and may have to exercise the rest at once. Selling to a third party is not permitted, and because they cannot be sold they tend to be exercised earlier than an equivalent exchange-traded option. Start-ups unable to match established salaries lean on them heavily. Whether such grants align executives with shareholders is arguable: a rising share price rewards both, but a falling one hurts shareholders far more, since their capital is real while the options merely expire worthless.
Accounting once made these grants look free. An option struck at the current stock price had no effect on reported profit, which made it an attractive way to pay senior management and created an incentive to cheat on the grant date. A firm whose stock had climbed from USD 42 to USD 50 over the past week could backdate an at-the-money grant by three weeks, set the strike at USD 42, and hand executives extra value at no accounting cost. This practice, known as backdating, was illegal then and remains so, and academic work found it was once widespread. The Securities and Exchange Commission now requires grants to be reported within two business days, and options must be valued and expensed at issue, so many companies award shares instead.