stock options and trading strategies
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Stock Options and Trading Strategies. Finance (Derivative Securities) 312 Tuesday, 12 September 2006 Readings: Chapters 9 & 10. Notation. c : European call option price p :European put option price S 0 :Stock price today K :Strike price T :Life of option - PowerPoint PPT PresentationTRANSCRIPT
Stock Options and Stock Options and Trading StrategiesTrading Strategies
Finance (Derivative Securities) 312
Tuesday, 12 September 2006
Readings: Chapters 9 & 10
NotationNotation c : European call option price p : European put option price S0: Stock price today K : Strike price T : Life of option : Volatility of stock price C : American Call option price P : American Put option price ST: Stock price at option maturity D : Present value of dividends during option’s life r : Risk-free rate for maturity T with cont comp
Factors Influencing Factors Influencing ValueValue
c p C PVariable
S0
KTrD
+ + –+
? ? + ++ + + ++ – + –
–– – +
– + – +
Upper and Lower BoundsUpper and Lower Bounds
Call Options• Stock price is upper bound for both American
and European
Put Options• Exercise price is upper bound for both
American and European (PV of K)
Upper and Lower BoundsUpper and Lower Bounds
Suppose that
c = 3 S0 = 20
T = 1 r = 10%
K = 18 D = 0
Is there an arbitrage opportunity?
Upper and Lower BoundsUpper and Lower Bounds
Lower Bound for European Call Options • c S0 –Ke –rT (non-dividend paying)
• Since S0 –Ke –rT = $3.71, and c = $3, opportunity for arbitrage exists
• Short stock, buy call, invest proceeds• If stock price > $18, profit = $0.79• If stock price < $18, profit = $1.79
Upper and Lower BoundsUpper and Lower Bounds
Suppose that
p = 1 S0 = 37
T = 0.5 r = 5%
K = 40 D = 0
Is there an arbitrage opportunity?
Upper and Lower BoundsUpper and Lower Bounds
Lower Bound for European Put Options • p Ke–rT – S0
(non-dividend paying)• Since Ke–rT – S0 = $2.01, and p = $1,
opportunity for arbitrage exists• Borrow p + S0 , buy stock, repay loan• If stock price < $40, profit = $1.04• If stock price > $40, profit = $3.04
Put-Call ParityPut-Call Parity
Consider strategy I:
Buy a share, and buy a put option
ST ≤ K ST > K
Buy Stock ST ST
Buy Put K – ST 0
Total K ST
Put-Call ParityPut-Call Parity
Consider strategy II:
Buy a call option, and borrow Ke–rT
ST ≤ K ST > K
Buy Call 0 ST – K
Invest Ke–rT K K
Total K ST
Put-Call ParityPut-Call Parity
If two portfolios provide the same return, they must cost the same to set up, otherwise an opportunity for arbitrage exists
p + S0 = c + Ke–rT
American OptionsAmerican Options
Early exercise of calls (non-dividend paying)• Insurance• Time value
Early exercise of puts (non-dividend paying)• Insurance worth forgoing
Effect of DividendsEffect of Dividends
Consider strategy I:
Buy a put, a share, and borrow D + Ke–rT
ST ≤ K ST > K
Buy Share ST ST
Buy Put K – ST 0
Borrow D+Ke-rT –K –K
Total 0 ST – K
Effect of DividendsEffect of Dividends
Consider strategy II:
Buy a call
ST ≤ K ST > K
Buy Call 0 ST – K
Total 0 ST – K
p + S0 = c + D + Ke–rT
Protective PutProtective Put
Buy stock, worth $50Buy put option, exercise price $53,
premium $5Used when the investor is worried the
stock price will fallPut option provides insurance against loss
on the stock
Protective PutProtective Put
At expiry:
ST Payoff (Stock + Put) Profit 45 -5 + 8 = 3 3 - 5 = -2
50 0 + 3 = 3 3 - 5 = -255 5 + 0 = 5 5 - 5 = 060 10 + 0 = 10 10 - 5 = 565 15 + 0 = 15 15 - 5 = 1070 20 + 0 = 20 20 - 5 = 15
Protective PutProtective PutProfit
0ST-2
-50
48Stock
Put Option
Protective Put
Breakeven point
-5
48 50 53 55
Covered CallCovered Call
Buy stock, worth $50Write call option, exercise price $60,
premium $5Used to boost income with premiums
collected, and locks in a selling price (though potential capital gains are forfeited)
Covered CallCovered Call
At expiry:
ST Payoff Profit 30 -20 -15 40 -10 -5 50 0 5 60 10 15 70 10 15 80 10 15
Covered CallCovered CallProfit
0 ST
5
-50
45 50 60 65
Stock
Call Option
Covered Call 15
-45
Breakeven point
StraddlesStraddles
Buy call and put with same exercise priceUsed when share price is expected to
move, but direction uncertainFor short straddle, sell call and put
StranglesStrangles
Buy out-of-the-money call and put, where XC > XP
Similar to straddle, but price needs to move by greater amount in order to breakeven
Costs less than straddleFor short strangle, sell call and put
Strips and StrapsStrips and Straps
Strip is a bearish straddleBuy 2 puts and 1 call with same X
Strap is a bullish straddleBuy 1 put and 2 calls with same X
Butterfly SpreadButterfly Spread
Buy put option with relatively low exercise price (X1)
Buy call option with a relatively high exercise price (X3)
Sell a put option and a call option with an exercise price between X1 and X3 (X2)