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1、Basics of Stock Options,Timothy R.Mayes,Ph.D.FIN 3600:Chapter 15,Introduction,Options are very old instruments,going back,perhaps,to the time of Thales the Milesian(c.624 BC to c.547 BC).Thales,according to Aristotle,purchased call options on the entire autumn olive harvest(or the use of the olive p
2、resses)and made a fortune.Joseph de la Vega(in“Confusin de Confusiones,”1688,104 years before the NYSE was founded under the buttonwood tree)also wrote about how options were dominating trading on the Amsterdam stock exchange.Dubofsky reports that options existed in ancient Greece and Rome,and that
3、options were used during the tulipmania in Holland from 1624-1636.In the U.S.,options were traded as early as the 1800s and were available only as customized OTC products until the CBOE opened on April 26,1973.,What is an Option?,A call option is a financial instrument that gives the buyer the right
4、,but not the obligation,to purchase the underlying asset at a pre-specified price on or before a specified dateA put option is a financial instrument that gives the buyer the right,but not the obligation,to sell the underlying asset at a pre-specified price on or before a specified dateA call option
5、 is like a rain check.Suppose you spot an ad in the newspaper for an item you really want.By the time you get to the store,the item is sold out.However,the manager offers you a rain check to buy the product at the sale price when it is back in stock.You now hold a call option on the product with the
6、 strike price equal to the sale price and an intrinsic value equal to the difference between the regular and sale prices.Note that you do not have to use the rain check.You do so only at your own option.In fact,if the price of the product is lowered further before you return,you would let the rain c
7、heck expire and buy the item at the lower price.,Options are Contracts,The option contract specifies:The underlying instrumentThe quantity to be deliveredThe price at which delivery occursThe date that the contract expires Three parties to each contractThe BuyerThe Writer(seller)The Clearinghouse,Th
8、e Option Buyer,The purchaser of an option contract is buying the right to exercise the option against the seller.The timing of the exercise privilege depends on the type of option:American-style options can be exercised any time before expirationEuropean-style options may only be exercised during a
9、short window before expirationPurchasing this right conveys no obligations,the buyer can let the option expire if they so desire.The price paid for this right is the option premium.,The Option Writer,The seller of an option contract is accepting the obligation to have the option exercised against he
10、r,and receiving the premium in return.If the option is exercised,the seller must:If it is a call,sell the stock to the option buyer at the exercise price(which will be lower than the market price of the stock)If it is a put,buy the stock from the put buyer at the exercise price(which will be higher
11、than the market price of the stock),The Role of the Clearinghouse,The clearinghouse(the Options Clearing Corporation)exists to minimize counter-party riskThe clearinghouse is a buyer to each seller,and a seller to each buyerBecause the clearinghouse is well diversified and capitalized,the other part
12、ies to the contract do not have to worry about default.Additionally,since it takes the opposite side of every transaction,it has no net risk(other than the small risk of default on a trade).Also handles assignment of exercise notices,Examples of Options,Direct options are traded on:Stocks,bonds,futu
13、res,currencies,etc.There are options embedded in:Convertible bondsMortgagesInsurance contractsMost corporate capital budgeting projectsetc.Even stocks are options!,Option Terminology,Strike(Exercise)Price-this is the price at which the underlying security can be bought or soldPremium-the price which
14、 is paid for the option.For equity options this is the price per share.The total cost is the premium times the number of shares(usually 100).Expiration Date This is the date by which the option must be exercised.Usually the Saturday following the third Friday of the month.In practice,this means the
15、third Friday.Moneyness This describes whether the option currently has an intrinsic value above 0 or not:In-the-Money for a call this is when the stock price exceeds the strike price,for a put this is when the stock price is below the strike priceOut-of-the-Money for a call this is when the stock pr
16、ice is below the strike price,for a put this is when the stock price exceeds the strike priceAmerican-style-options which can be exercised before expirationEuropean-style-options which cannot be exercised before expiration,The Intrinsic Value of Options,The intrinsic value of an option is the profit
17、(not net profit!)that would be received if the option were exercised immediatelyFor call options:IV=max(0,S-X)For put options:IV=max(0,X-S)At expiration,the value of an option is its intrinsic valueBefore expiration,the market value of an option is the sum of the intrinsic value and the time valueSi
18、nce options can always be sold before expiration,it is never optimal to exercise them early.If you did so,you would lose the time value.Youd be better off to sell the option,collect the premium,and then take your position in the underlying security.,Profits from Buying a Call,Selling a Call,Profits
19、from Buying a Put,Selling a Put,Combination Strategies,We can construct strategies consisting of multiple options to achieve results that arent otherwise possible,and to create cash flows that mimic other securitiesSome examples:Buy WriteStraddleSynthetic Securities,The Buy-Write Strategy,This strat
20、egy is more conservative than simply owning the stockIt can be used to generate extra income from stock investmentsIn this strategy we buy the stock and write a call,The Straddle,If we buy a straddle,we profit if the stock moves a lot in either directionIf we sell a straddle,we profit if the stock d
21、oesnt move much in either directionThis straddle consists of buying(or selling)both a put and call at the money,Synthetic Securities,With appropriate combinations of the stock and options,we can create a set of cash flows that are identical to puts,calls,or the stockWe can create synthetic:Long Stoc
22、k Buy Call,Sell PutLong Call Buy Put,Sell StockLong Put Buy Call,Sell StockShort Stock Sell Call,Buy PutShort Call Sell Put,Buy StockShort Put Sell Call,Buy StockThe reasons that this works requires knowledge of Put-Call Parity,Put-Call Parity,Put-Call parity defines the relationship between put pri
23、ces and call prices that must exist to avoid possible arbitrage profits:In other words,a put must sell for the same price as a long call,short stock and lending the present value of the strike price(why?)By manipulating this equation,we can see how to create synthetic securities(in the above form it
24、 shows how to create a synthetic put option),Put-Call Parity Example,Assume that we find the following conditions:S=100X=100r=10%t=1 yearC=16.73P=?,Synthetic Long Stock Position,We can create a synthetic long position in the stock by buying a call,selling a put,and lending the strike price at the ri
25、sk-free rate until expiration,Synthetic Long Call Position,We can create a synthetic long position in a call by buying a put,buying the stock,and borrowing the strike price at the risk-free rate until expiration,Synthetic Long Put Position,We can create a synthetic long position in a put by buying a
26、 call,selling the stock,and lending the strike price at the risk-free rate until expiration,Synthetic Short Stock Position,We can create a synthetic short position in the stock by selling a call,buying a put,and borrowing the strike price at the risk-free rate until expiration,Synthetic Short Call P
27、osition,We can create a synthetic short position in a call by selling a put,selling the stock,and lending the strike price at the risk-free rate until expiration,Synthetic Short Put Position,We can create a synthetic short position in a put by selling a call,buying the stock,and borrowing the strike
28、 price at the risk-free rate until expiration,Option Valuation,The value of an option is the present value of its intrinsic value at expiration.Unfortunately,there is no way to know this intrinsic value in advance.The most famous(and first successful)option pricing model,the Black-Scholes OPM,was de
29、rived by eliminating all possibilities of arbitrage.Note that the Black-Scholes models work only for European-style options.,Option Valuation Variables,There are five variables in the Black-Scholes OPM(in order of importance):Price of underlying securityStrike priceAnnual volatility(standard deviati
30、on)Time to expirationRisk-free interest rate,Variables Affect on Option Prices,Call OptionsDirect InverseDirectDirectDirect,Put OptionsInverseDirectDirectInverseDirect,VariableStock PriceStrike PriceVolatilityInterest RateTime,Option Valuation Variables:Underlying Price,The current price of the unde
31、rlying security is the most important variable.For a call option,the higher the price of the underlying security,the higher the value of the call.For a put option,the lower the price of the underlying security,the higher the value of the put.,Option Valuation Variables:Strike Price,The strike(exerci
32、se)price is fixed for the life of the option,but every underlying security has several strikes for each expiration monthFor a call,the higher the strike price,the lower the value of the call.For a put,the higher the strike price,the higher the value of the put.,Option Valuation Variables:Volatility,
33、Volatility is measured as the annualized standard deviation of the returns on the underlying security.All options increase in value as volatility increases.This is due to the fact that options with higher volatility have a greater chance of expiring in-the-money.,Option Valuation Variables:Time to E
34、xpiration,The time to expiration is measured as the fraction of a year.As with volatility,longer times to expiration increase the value of all options.This is because there is a greater chance that the option will expire in-the-money with a longer time to expiration.,Option Valuation Variables:Risk-
35、free Rate,The risk-free rate of interest is the least important of the variables.It is used to discount the strike price,but because the time to expiration is usually less than 9 months(with the exception of LEAPs),and interest rates are usually fairly low,the discount is small and has only a tiny e
36、ffect on the value of the option.The risk-free rate,when it increases,effectively decreases the strike price.Therefore,when interest rates rise,call options increase in value and put options decrease in value.,Note,The following few slides on the Black-Scholes model will not be tested.I consider the
37、 use of these models to be beyond the scope of this course.I am including this information only for those interested.,The Black-Scholes Call Valuation Model,At the top(right)is the Black-Scholes valuation model for calls.Below are the definitions of d1 and d2.Note that S is the stock price,X is the
38、strike price,s is the standard deviation,t is the time to expiration,and r is the risk-free rate.,B-S Call Valuation Example,Assume a call with the following variables:S=100X=100r=0.05 s=0.10t=90 days=0.25 years,The Black-Scholes Put Valuation Model,At right is the Black-Scholes put valuation model.The variables are all the same as with the call valuation model.Note:N(-d1)=1-N(d1),B-S Put Valuation Example,Assume a put with the following variables:S=100X=100r=0.05 s=0.10t=90 days=0.25 years,
