Mechanics of Options Markets

The Difference of the Contractsaction cost

option contrac

ts

gives the holder of the option the right to do something.

the purchase of an option requires an up-front payment.

forward and

future contrac

ts

the two parties have committed themselves to some action.

it cost nothing (except for the margin requirements) to enter into a forward or futures contract.

Types of Options(1/2)

● Expiration date：● American Option: it can be exercised at any time up to the expiration date.● European Option: it can be exercised only on the expiration date.

● Call option: gives the holder of the option the right to buy an asset by a certain date for a certain price.

● Put option: gives the holder of the option the right to sell an asset by a certain date for a certain price.

Types of Options(2/2) ● Right：

Option Positions(1/6):long calloption price=5 ,K=100 ,T=4 months.

30

20

10

0-5

70 80 90 100

110120130

profit

terminal Stock price

1.S<100 …… not to exercise

ex: S=98, 0*(98-100)-5*100=-

500 2.S>105 …… exercise ex: S=115, 100*(115-100)-

5*100=1000 3. 100<S<105 …… exercise ex: S=102, 100*(102-100)-

5*100=-300

● In general, call options should always be exercised at the expiration date if the stock price is above the strike price.

Option Positions(2/6):long putoption price=7 ,K=70 ,T=3 months.

30

20

10

0

-770605040 80 90 100

profit

terminal stock price

1.S>70 …… not to exercise

ex: S=80, 0*(70-80)-7*100=-

7002.S<63 …… exercise ex: S=55, 100*(70-55)-

7*100=800 3. 63<S<70 …… exercise ex: S=65, 100*(70-65)-

7*100=-200

● In general, put options should always be exercised at the expiration date if the stock price is under the strike price.

Option Positions(3/6):short call

option price=5 ,K=100 ,T=4 months.

-30

-20

-10

05

70 80 90 100

110 120 130

profit

terminal stock price

Option Positions(4/6):short put

option price=7 ,K=70 ,T=3 months.

-30

-20

-10

7

070

605040

80 90 100

profit

terminal stock price

Option Positions(5/6) K =strike price, ST =final price of underlying asset.

Payoff

KKSTST

PayoffLong call Short

call

max(ST-K,0) -max(ST-k,0)=min(K-ST,0)

K =strike price, ST =final price of underlying asset.

K KSTST

Payoff PayoffLong put Short put

Option Positions(6/6)

max(K-ST,0) -max(K-ST,0)=min(ST-K,0)

Underlying Assets(1/2) ● Stock options:

● Foreign currency options: (Ch15)

One contract gives the holder the right to buy or sell 100 shares at the specified

strike price. This contract size is

convenient because the shares themselves are

normally traded in lots of 100.

The major exchange for trading foreign currency options is the Philadelphia Stock Exchange. The size of one contract depends on the currency.

Underlying Assets(2/2)

● Index options: (Ch15)

● Futures options: (Ch16) ● When call option is exercised, long future

plus future price over strike price. ● When put option is exercised, short future plus strike price over future price.

● Settlement is always in cash, rather than by delivering the portfolio underlying the index. ● One call contract on the S&P 100,K=980,ST=992, the writer of the contract pays the holder (992-980)*100=1200.

Specification of Stock Options(1/8)

● Expiration dates(1/2):● The last day on which options trade is the third Friday of the expiration month 4:30 p.m.

● The precise expiration date is the third Saturday of the expiration month 10:59 p.m.

● Stock options are on a January, February, or March cycle.

● January cycle: Jan, Apr, Jul, Oct.

● February cycle: Feb, May, Aug, Nov.

● March cycle: Mar, Jun, Sep, Dec.

Specification of Stock Options(2/8)

● If the expiration date has not been reached, options trade in the current month, the following month, and next two months in the cycle.

● If the expiration date has passed, options trade in the next month, the next-but-one month, and next two months in the cycle.

● LEAPS (long-term equity anticipation securities) have expiration dates up to 39 months. The expiration dates for LEAPS are always in January.

● Expiration dates(2/2):

● Strike prices:● 5 < S < 25 ……spaced 2.5

● 25 < S < 200 ……spaced 5

● S > 200 ……spaced 10 ● Stock splits and stock

dividends can lead to nonstandard strike prices.

Specification of Stock Options(3/8)

● Terminology(1/2):

Specification of Stock Options(4/8)

call put in the money S > K S < Kat the money S = K S = K out of the money S < K S > K

option

class

all options of the same type (calls or puts) are referred to as an option class.

option

series

an option series consists of all the options of a given class with the same expiration date and strike price.

● The intrinsic value of an option is defined as the maximum of zero and the value the option would have if it were exercised immediately.

● Often it is optimal for the holder to wait rather than exercise immediately. The option is said to have time value.

● The total value of an option can be thought of as the sum of its intrinsic value and its time value.

Specification of Stock Options(5/8)● Terminology(2/2):

● Dividends and stock splits(1/2): ● Exchange-traded options are not usually adjusted for cash dividends.

● Exchange-traded options are adjusted for stock splits. After an n-for-m stock split, the strike price is reduced to m/n of its previous value, and number of shares covered by one contract is increased to n/m of its previous value.

Specification of Stock Options(6/8)● FLEX option: These are options where the traders on the floor of the exchange agree to nonstandard terms.

● Stock options are adjusted for stock dividends. ● example 8.2: N=100 ,K=15 , declares a 25% stock dividend .This is equivalent to a 5-for-4 stock split. 5/4 * 100 = 125 (shares) 4/5 * 15 = 12 (per share)

Specification of Stock Options(7/8)● example 8.1: N=100 ,K=30 , makes a 2-for-1 stock split. 2/1 * 100 = 200 (shares) 1/2 * 30 = 15 (per share)

● Dividends and stock splits(2/2):

Specification of Stock Options(8/8)● Position limits: This defines the maximum number of option contracts that an investor can hold on one side of the market.

● Exercise limits: It defines the maximum number of contracts that can be exercised by any individual in any period of five consecutive business days.

Trading● Market makers: (Ch17) ● A market maker is an individual who will quote both a bid and an offer price on the option. ● The offer is always higher than the bid, and the amount by which the offer exceeds the bid is referred to as the bid-offer spread. ● Market makers therefore add liquidity to the market.

long an

option

an investor who has purchased an option can close out the position by issuing an offsetting orders to sell the same option.

short an

option

an investor who has written an option can close out the position by issuing an offsetting orders to buy the same option.

Commissions(1/2)● Discount brokers generally charge lower commissions than full-service brokers. The actual amount charged is often calculated as a fixed cost plus a proportion of the dollar amount of the trade.example : the purchase of eight contracts when the

option price is 3 cost 20+(0.02*2400)=68 in commission. Dollar

amount of trade

<2500 2500 to 10000

>10000

Commission

20 +2% of dollar amount

45 +1% of dollar amount

120 +0.25% of dollar amount

Table 8.1 A typical commission schedule for discount broker.

● If option position is closed out by entering into an offsetting trade, the commission must be paid again. If the option is exercised, the commission is the same to buy or sell the underlying stock.example : an investor buys one call, K=50, S0=49, option price is 4.5.Suppose the stock reaches 60,pays 1.5% commission cost 30 *+(0.015*60*100)=120 ,and the net profit is 1000-450-120=430

Commissions(2/2)

*both the max and min commission is 30 for the first contract.● A hidden cost in option trading (and in stock trading) is the market maker’s bid-offer spread. Suppose the bid price was 4,and offer price was 4.5,we can assume fair price is halfway between bid and offer price, or 4.25.

Margins(1/2)

● An investor can borrow up to 50% of the price from the broker .This is known as buying on margin.

● When call and put options with maturities less than 9 months are purchased, the option price must be paid in full.

● Writing naked option:● A naked option is an option that is not combined with an offsetting position in the underlying stock.

● example 8.3 : an investor writes four naked call option, option price=5, K=40, S=38, and the option is 2 out of the money.

400*(5+0.2*38-2)= 4240 , 400*(5+0.1*38)= 3520. The initial margin is 4240.If the option had been a put , 400*(5+0.2*38)= 5040 , 400*(5+0.1*40)= $3600. The initial margin is 5040.

Margins(2/2)a written naked call option

100% of the proceeds of the sale plus 20% of the underlying share price less the amount which the option is out of money

100% of the proceeds of the sale plus 10% of the underlying share price

a written naked put option

100% of the proceeds of the sale plus 20% of the underlying share price less the amount which the option is out of money

100% of the proceeds of the sale plus 10% of the exercise price

The Option Clearing Corporation● The Option Clearing Corporation (OCC) performs much the same function for options markets as the clearinghouse does for futures markets.(Ch2)

● Exercising an Option:

● The OCC has a number of members ,and all option trades must be cleared through a member.

● An investor notifies a broker to exercise an option.● The broker turn notifies the OCC member.● This member places an exercise order with the OCC.● The OCC selects a member with outstanding short option in the same option.● The member selects a investor who has written option.

Regulation

● Options markets are regulated in a number of different ways.

● Both the exchange and its Option Clearing Corporation have rules governing the behavior of traders.

● Options markets have demonstrated a willingness to regulatory authorities.

Taxation(1/2)● For both the holder and the writer of a stock option, a gain or loss is recognized when (a) the option expires unexercised or (b) the option position is closed out.

● If the option is exercised, the gain or loss from the option is rolled into the position taken in the stock and recognized when stock position is closed out.

● Wash sale rule :● An investor who buys a stock what the price is 60. If the stock price drops to 40,the investor might be tempted to sell the stock and immediately repurchase it, so that the 20 loss is realized for tax purchases.

● The tax authorities have ruled that when the repurchase is within 30 days of the sale, any loss on the sale is not deductible.

● Constructive sales :An appreciated property is now treated as “ constructively sold” when the owner does one of the following :

Taxation(2/2)

● Enter into a short sale of the same or substantially identical property.● Enter into a futures or forward contract to deliver the same or substantially identical property.● Enter into one or more positions that eliminate substantially all of the loss and opportunity for gain. It should be noted that transactions reducing only

the risk of loss or only the opportunity for gain should not result in constructive sales.

Warrants, Employee Stock Options,and Convertibles

● Convertibles:

● Employee stock options :

● Warrants:Warrants are options issued by a financial institution or nonfinancial corporation.

Employee stock options are call option issued to executives by their company to motivate them to act in the best interests of the company’s shareholders.

Convertibles bonds are bonds issued by a company that can be converted into equity at certain times using a predetermined exchange ratio.

Over-The-Counter Options Markets

● The chief potential disadvantage of the over-the-counter markets is that option writer may default. This means that the purchaser is subject to some credit risk.

● The over-the-counter market for options has become important since the early 1980s and is now larger than the exchange-traded market.

● The instruments traded in the over-the-counter market are often structured by financial institutions to meet the precise needs of their clients. The option is then referred to as an exotic option.(Ch24)

Summary(1/2)● There are four possible position in options markets: long call, short call, long put, shot put.

● Options are currently traded on stocks, stock indices, foreign currencies, futures contracts.

● An exchange must specify the size of the contract, the expiration time, and the strike price.

● The terms of a stock option are not adjusted for cash dividends. However, they are adjusted for stock dividends ,stock splits, and rights issues.

● A market maker is an individual who is prepared to quote both a bid price and an offer price.

● Writers of options have potential liabilities and are required to maintain margins with their broker.

● The Options Clearing Corporation is responsible for keeping a record of all outstanding contracts, handing exercise orders, and so on.

● An advantage of over-the-counter options is that they can be tailored by a financial institution to meet the particular needs of a corporate treasurer or fund manager.

Summary(2/2)