411 - exam 2 Flashcards
Call options
holder has right to buy asset by certain date for certain price
–Euro. options can ONLY EXERCISE AT EXPIRATION DATE
ex. call option to purchase 100 shares with strike $100 - current stock price is 98 - 5 mo. maturity – one share is $5
- -so initial investment is 5 * 100 = 500
if stock price is less than 100, investor will not exercise - so lose 500
if stock price > 100 – option exercised and earns profit (ex. 115 - 15 * 100 = 1500)
but if stock price is 102 - $2 profit per share so earn $200 - but lost $300 when consider the 500 investment in the options
put option
holder has right to sell asset at certain date for certain price
—hopes stock price will go down!
ex. euro strike 70 to sell 100 shares of stock - current stock price is 65 and option price is 7
- -initial investment is 7 * 100 = 700
- -breakeven if price is 63 - bc make $7 per share in exercising option but then take out 7 initial investment
- -if price is 55 - exercise and earn 15 per share = 1500 - 700 investment = 800 profit
maturity date = expiration date
exercise or strike price
4 types of option positions
2 sides of every option contract
- -short position also called (investor who was WRITTEN or SOLD the option)
- -writer = rec. cash up front but has risk later depending on price movements
- -writer’s profit and loss is opposite of the purchaser of the option
payoffs for option positions
- long call
- –payoff is MAX(ST - K, 0) - short call
- -payoff is -MAX(ST - K, 0)
- -OR MIN(K-St, 0) - long put
- -MAX(K - ST, 0) - short put
- –MAX(K - ST, 0)
- -OR MIN(ST - K, 0)`
Option trading
–expiration time
most on exchanges
- -CBOE (chicago board options exchange)
- -ONE CONTRACT gives holder right to buy/sell 100 SHARES at specified price
- expiration dates
- -the month in which expiration occurs - Jan. call on IBM expires in January
- -precise expiration date is the THIRD FRIDAY OF EXPIRATION MONTH
- —trading takes place every business day (8:30am-3pm, Chicago time) until it expires
in US stock options - they are on Jan., Feb., Mar. cycle
- -Jan cycle has months Jan. Apr. July. .Oct (every 3 mo.)….etc.
- -same for others but starts in Feb. or Mar.
if expiration of currentmonth has passed - options trade with expiration dates of next month, the next but one month and the next 2 months of the cycle
—ex. Jan. cycl at beg. of Jan. -traded with expiration dates in Jan., Feb. April. and July
LT options called LEAPS
option terminology
- -option class
- -option series
- -in the money
- -at the money
- -out of the money
- -intrinsic value
- -time value
option class - all options of same type (so IBM calls are one class and IBM puts are another class)
option series – consists of all options of a given class with SAME expiration and SAME strike (IBM 180 Oct. 2015 calls)
in the money - if stock is in the money the stock price is in a place where option could be exercised (C –> S > K)
out of the money - can’t be exercised (C –> S < K)
at the money (S = K)
intrinsic value = max. of zero and payoff if option were exercised IMMEDIATELY
time value = the excess of option’s value over its intrinsic value
—TOTAL VALUE OF OPTION is sum of its intrinsic value and time value
dividends and option terms
exchange traded options are not usually adjusted for cash dividends - no adjustments to terms of contract
—but there is exception for LARGE cash div. (usually 10% of stock price)
stock options ARE adjusted for STOCK dividends - involves comp. issuing more shares to its existing shareholders
- -ex. a 20% stock dividend means investors rec. one new share for each 5 already owned
- -sames as 6 for 5 stock split
- -stock price goes down as a result (down 5/6 its orig. value)
ex. put option to sell 100 shares of comp. for $15 per share
- –comp. declares a 25% stock dividend = 1 new share for every 4 – or 5 for 4 stock split
- –so now stock price goes down 4/5 = so right to sell 125 shares for $12 each
stock splits
exchange traded options are adjusted for stock splits == existing shares are “split” into more shares
3 for 1 stock split - when three new shares replace one existing share – stock price goes down 1/3 of prev. value
so if call options to buy 100 shares of comp. for $30 per share - company makes 2 for 1 stock split
—now terms of option change to right to buy 200 shares for $15 each
market makers
- big
- offer
- big offer spread
most option exchanges use mkt. makers to facilitate trading - an indiv. who will quote both the bid and offer price
- -BID = price at which mkt. maker is prepared to buy
- -OFFER = price at which mkt. maker is prepared to see
bid-offer spread = offer is always higher than the bid – amt. diff. called spread
–the exchange sets limits for the spreads
offsetting order - inv. who has purchased an option can close out position by issuing an offsetting order to sell the same option
margin req. on naked options
in US - when shares ar epurchased or inv. pays cash or borrows using a margin acct. = called BUYING ON MARGIN
- -initial margin is usually 50% of value of shares and maintenance margin is 25% value of shares
- -if T on option is < 9 mo. need to pay full - but if greater than 9 mo. can use margin acct.
NAKED OPTIONS - option that is not combined with offsetting position in the underlying stock
GREATER OF THE 2 (call option)
- 100% of sale proceeds + 20% of underlying share price - amt. out of the money
- 100% sale proceeds + 10% underlying price
NAKED PUT OPTION
- 100% of sale proceeds + 20% underlying share price - amt. out of money
- 100% sale proceeds + 10% exercise price
covered call
OCC
covered call = written call option when shares that might have to be delivered are already owned - no margin req. - less risky
OCC - options clearing corp. - performs same function for option mkt. as clearinghouse in futures mkt.
- -guarantees writers fulfill contract terms
- -when an option is exercised – open interest goes down by 1
diff. btwn warrants, employee stock options, convertible bonds
- -# options issued are predetermined!!!! - wwhereas a trading option on CBOE is not predetermined
- -in above 3 types - the comp. will issue new shares and inc. its number shares outstanding
fair price for option
would be half way btwn bid and offer price quoted by mkt. maker
- -bc buy at offer and sell at the bid
- each time they buy or sell - there is a HIDDEN cost = to half the bid-offer spread!
factors that affect option prices - THE BIG 6
- current stock price
- -CALL - payoff is amt. stock price exceeds strike price=. so more valuable as stock price goes up
- -PUT - opposite - strike price
- time to expiration
- -both PUT AND CALL AMERICAN options are more valuable as time to expiration increases
- -euro. - not always true bc have to wait to exercise and if div. paid dec. stock price and potential payoff - volatility
- -volatility goes up = inc value
- -all option types benefit from volatility bc of limited downside risk - rf rate
- -if goes up = prices fall = inc. value of put
- -if rf goes down = prices up = inc. value of call - div.
- -reduce stock price = bad for call but good for put
upper bounds of option prices
Upper bounds for both Euro. and Am. calls is So!!!!! stock price
–or arbitrage bc could buy the stock and then sell the call
American put option – gives right to sell one share for K – no matter how low stock price goes, can never be worth more than K
–euro. options same!! but cannot be worth more than PV of K today = ke^-rT
if wasn’t true - arbitrage bc sell option and inv. proceeds at rf rate
put-call parity
relationship btwn prices of Euro. put and call options with SAME STRIKE and SAME MAUTURITY
C + Ke^-rT = p + So
–shows value of euro. call with certain exercise price and date can be solved from value of euro. put with same exrcise and date
ONLY WORKS FOR EURO. OPTIONS – similar for american if there are NO dibidends!!
in put-call parity
A. portfolio with one euro. call and zero cpn. bond with payoff K at time T
C. portfolio with one euro. put and one share of stock
covered call
protective put
long position in stock and short position in euro. call
- –so if stock price goes above strike and option is exercised - you already have the stock
- -and if price goes down call is not exercised but you can sell the stock and keep profits from call
buy Euro. put on stock and the stock itself
- -if prices go up you don’t exercise put but sell high at mkt. prices
- -if prices go down you can exercise the put and short the stock
GRAPHS
COVERED CALL
—look like a SHORT PUT graph
(loss if low prices but crosses line then at K straight bc will not exercise)
PROTECTIVE PUT
–looks like a LONG CALL
(below line as loss until cross K and becomes a gain as price increases)
opposite positions are just flipped!!!!!
Bull spreads
HOPING STOCK PRICE WILL INCREASE!!!!
- –buy euro. call at K1 and sell K2 call
- -buy low sell high!!!!
- -BOTH OPTIONS HAVE SAME EXPIRATION DATE
BULL looks like an S!!! Kinks at both Ks and crosses the stock price line between K1 and K2
Bear spread!!!!
Hoping price will go DOWN!!!!!
- –buy K2 and short K1
- -buy high and sell low
- –looks like a Z where kinks at each k and crosses btwn them
butterfly spread
OPTIONS WITH THREE DIFF. Ks
- –buy K1 and K3 and short 2 at K2
- -hoping not to have large price changes – give sprofit if stays close to K2 but only small loss if it moves in either directions
- -use when think large stock movements are unlikely
Staddle
buy euro call and euro put with same strike and same expiration!!!!
- –use when think there WILL BE a large price movement!!!!
- -but if stays close you have large loss
bottom straddle or strdle purchase
top straddle/straddle write is opposite and it sells call and put with same price and expiration - opp. where only profit if stock price on expiration is close to strike!!!
strangle
called BOTTOM VERTICLE COMBO
- –buy euro. call at K2 and buy put at K1
- –buy higher call!!!!!
- –still think there will be large price movements but minimizes your downside risk
strips and straps
STRIP
- -long one euro. call and long 2 euro. puts with same strike and T
- –inv. is betting there will be large price movement but more likely an DECREASE
STRAP
- -long 2 calls and one put
- -same but expect price to go up!!!
Binomial trees
NO ATRBITRAGE
and risk-neutral assumpyion
- expected return on stock is rf rate
- discount rate for expected payoff on option is rf rate
BSM
Black Scholes Merton model
- -helped pricing an dheding options
- -won nobel prize in 1997
BSM uses CAPM to see relationship btwn mkt.s req. return on option and req. return on stock
–depends on stock price and time
Merton came in and set up a riskless portfolio of the option and the stock!!
volatility found by historical data or implied option prices
st.dev = measure of uncertainty about the returns provided by the stock
volatility of stock price
the st. dev. of return provided by stock in one year when return is using cont. compounding
our uncertainty about future stock price (st. dev.) increases with sq. rt of how far ahead we are looking
–stock price in 4 weeks is about twice st. dev. in one week (.3 * sq. rt 4) = .6
life of option calculated with trading days
number trading days until matrity/ 252
–3 mo. option = 90/252 = .3571 days
employee stock options
usually long life = 10-15 year contracts
–usually strike price is set = to stock price on grant date
vesting period - where options cannot be exercised (4 years)
- -when employees leave their jobs during vesting period they forfeit their options
- -if they leave after vesting period..they forfeit options if out of money and have to exercise if in the money
- -cannoy sell options
- -comp. issues new shares if they exercise
ok for employee options to be exercised early - bc can’t sell the optoins!! so better to use it
do options align interest of shareholders?
restrictued stock units (RSUs) best way - entitle employees to owns hare of company’s stock at particular future time – gains/losses on stock reflect gains/losses to employees
