Option-期权.ppt

1、金融市场学期权,攀 登,Buy - Long Sell - Short Call Put Key Elements Exercise or Strike Price Premium or Price Maturity or Expiration,Option Terminology,In the Money - exercise of the option would be profitable Call: market priceexercise price Put: exercise pricemarket price Out of the Money - exercise of the

2、option would not be profitable Call: market priceexercise price Put: exercise pricemarket price At the Money - exercise price and asset price are equal,Market and Exercise Price Relationships,American - the option can be exercised at any time before expiration or maturity European - the option can o

3、nly be exercised on the expiration or maturity date,American vs. European Options,Stock Options Index Options Futures Options Foreign Currency Options Interest Rate Options,Different Types of Options,Notation Stock Price = ST Exercise Price = X Payoff to Call Holder (ST - X) if ST X 0if ST X Profit

4、to Call Holder Payoff - Purchase Price,Payoffs and Profits on Options at Expiration - Calls,Payoff to Call Writer - (ST - X) if ST X 0if ST X Profit to Call Writer Payoff + Premium,Payoffs and Profits on Options at Expiration - Calls,Payoff Profiles for Calls,Payoffs to Put Holder 0if ST X (X - ST)i

5、f ST X Profit to Put Holder Payoff - Premium,Payoffs and Profits at Expiration - Puts,Payoffs to Put Writer 0if ST X -(X - ST)if ST X Profits to Put Writer Payoff + Premium,Payoffs and Profits at Expiration - Puts,Payoff Profiles for Puts,InvestmentStrategyInvestment Equity onlyBuy stock 100100 shar

6、es$10,000 Options onlyBuy calls 101000 options$10,000 LeveragedBuy calls 10100 options $1,000 equityBuy T-bills 2% $9,000 Yield,Equity, Options & Leveraged Equity,IBM Stock Price $95$105$115 All Stock$9,500$10,500$11,500 All Options$0 $5,000$15,000 Lev Equity $9,270 $9,770$10,770,Equity, Options & L

7、everaged Equity - Payoffs,IBM Stock Price $95$105$115 All Stock-5.0%5.0% 15% All Options-100% -50% 50% Lev Equity -7.3%-2.3% 7.7%,Equity, Options & Leveraged Equity,Protective Put,Use - limit loss Position - long the stock and long the put PayoffST X Stock ST ST Put X - ST 0,Protective Put Profit,ST

8、,Profit,-P,Stock Protective Put Portfolio,Covered Call,Use - Some downside protection at the expense of giving up gain potential Position - Own the stock and write a call PayoffST X Stock ST ST Call 0 - ( ST - X),Covered Call Profit,Straddle (Same Exercise Price) Long Call and Long Put Spreads - A c

9、ombination of two or more call options or put options on the same asset with differing exercise prices or times to expiration Vertical or money spread Same maturity Different exercise price Horizontal or time spread Different maturity dates,Option Strategies,ST X Payoff for Call Owned 0ST - X Payoff

10、 for Put Written-( X -ST) 0 Total Payoff ST - X ST - X,Put-Call Parity Relationship,Payoff of Long Call & Short Put,Since the payoff on a combination of a long call and a short put are equivalent to leveraged equity, the prices must be equal. C - P = S0 - X / (1 + rf)T If the prices are not equal ar

11、bitrage will be possible,Arbitrage & Put Call Parity,Stock Price = 110 Call Price = 17 Put Price = 5 Risk Free = 10.25% Maturity = .5 yr X = 105 C - P S0 - X / (1 + rf)T 17- 5 110 - (105/1.05) 12 10 Since the leveraged equity is less expensive, acquire the low cost alternative and sell the high cost

12、 alternative,Put Call Parity - Disequilibrium Example,Put-Call Parity Arbitrage,ImmediateCashflow in Six Months PositionCashflowST 105 Buy Stock-110 ST ST Borrow X/(1+r)T = 100+100-105-105 Sell Call+17 0-(ST-105) Buy Put -5105-ST 0 Total 2 0 0,Optionlike Securities,Callable Bonds Convertible Securit

13、ies Warrants Collateralized Loans,Exotic Options,Asian Options Barrier Options Lookback Options Currency Translated Options Binary Options,Intrinsic value - profit that could be made if the option was immediately exercised Call: stock price - exercise price Put: exercise price - stock price Time val

14、ue - the difference between the option price and the intrinsic value,Option Values,Time Value of Options: Call,FactorEffect on value Stock price increases Exercise price decreases Volatility of stock priceincreases Time to expirationincreases Interest rate increases Dividend Ratedecreases,Factors In

15、fluencing Option Values: Calls,Restrictions on Option Value: Call,Value cannot be negative Value cannot exceed the stock value Value of the call must be greater than the value of levered equity C S0 - ( X + D ) / ( 1 + Rf )T C S0 - PV ( X ) - PV ( D ),Allowable Range for Call,Call Value,S0,PV (X) +

16、PV (D),Upper bound = S0,Lower Bound = S0 - PV (X) - PV (D),100,200,50,Stock Price,Binomial Option Pricing:Text Example,Alternative Portfolio Buy 1 share of stock at $100 Borrow $46.30 (8% Rate) Net outlay $53.70 Payoff Value of Stock 50 200 Repay loan - 50 -50 Net Payoff 0 150,53.70,150,0,Payoff Str

17、ucture is exactly 2 times the Call,Binomial Option Pricing:Text Example,53.70,150,0,2C = $53.70 C = $26.85,Binomial Option Pricing:Text Example,Alternative Portfolio - one share of stock and 2 calls written (X = 125) Portfolio is perfectly hedged Stock Value50200 Call Obligation 0 -150 Net payoff50

18、50 Hence 100 - 2C = 46.30 or C = 26.85,Another View of Replication of Payoffs and Option Values,Generalizing the Two-State Approach,Assume that we can break the year into two six-month segments In each six-month segment the stock could increase by 10% or decrease by 5% Assume the stock is initially

19、selling at 100 Possible outcomes Increase by 10% twice Decrease by 5% twice Increase once and decrease once (2 paths),Generalizing the Two-State Approach,Assume that we can break the year into three intervals For each interval the stock could increase by 5% or decrease by 3% Assume the stock is init

20、ially selling at 100,Expanding to Consider Three Intervals,Expanding to Consider Three Intervals,Possible Outcomes with Three Intervals,EventProbabilityStock Price 3 up 1/8100 (1.05)3 =115.76 2 up 1 down 3/8100 (1.05)2 (.97)=106.94 1 up 2 down 3/8100 (1.05) (.97)2= 98.79 3 down 1/8100 (.97)3= 91.27,

21、Co = SoN(d1) - Xe-rTN(d2) d1 = ln(So/X) + (r + 2/2)T / (T1/2) d2 = d1 + (T1/2) where Co = Current call option value. So = Current stock price N(d) = probability that a random draw from a normal dist. will be less than d.,Black-Scholes Option Valuation,X = Exercise price. e = 2.71828, the base of the

22、 nat. log. r = Risk-free interest rate (annualizes continuously compounded with the same maturity as the option) T = time to maturity of the option in years ln = Natural log function Standard deviation of annualized cont. compounded rate of return on the stock,Black-Scholes Option Valuation,So = 100

23、X = 95 r = .10T = .25 (quarter) = .50 d1 = ln(100/95) + (.10+(5 2/2) / (5.251/2) = .43 d2 = .43 + (5.251/2) = .18,Call Option Example,N (.43) = .6664 Table 17.2 d N(d) .42 .6628 .43.6664 Interpolation .44.6700,Probabilities from Normal Dist,N (.18) = .5714 Table 17.2 d N(d) .16 .5636 .18.5714 .20.57

24、93,Probabilities from Normal Dist.,Co = SoN(d1) - Xe-rTN(d2) Co = 100 X .6664 - 95 e- .10 X .25 X .5714 Co = 13.70 Implied Volatility Using Black-Scholes and the actual price of the option, solve for volatility. Is the implied volatility consistent with the stock?,Call Option Value,P = C + PV (X) - So = C + Xe-rT - So Using the example data C = 13.70X = 95S = 100 r = .10T = .25 P = 13.70 + 95 e -.10 X .25 - 100 P = 6.35,Put Option Valuation: Using Put