Stock ABC sells for $64 and is not to pay any dividend in next year. Several 6-m
ID: 2721942 • Letter: S
Question
Stock ABC sells for $64 and is not to pay any dividend in next year. Several 6-month European options on MFN are listed below with their market prices:
Option
name
Type
Strike price
Market
price
N(d1)
N(d2)
A
Call
$60
8.4
0.70
0.62
B
Call
$65
5.8
C
Call
$70
3.7
D
Put
$60
3.0
E
Put
$65
5.1
F
Put
$70
If the stock price changes to $63.2, while other variables stay the same, what would be your estimates of the market price of Option D? (5 marks)Assume that Option B has a delta of 0.56. The probability that the option will be exercised on maturity date is 0.48. Use the B-S-M model to determine if Option B is overpriced, fairly priced, or underpriced? (5 marks)Suppose you short 100 Option B, how many shares do you need to hedge your position? (5 marks)
Option
name
Type
Strike price
Market
price
N(d1)
N(d2)
A
Call
$60
8.4
0.70
0.62
B
Call
$65
5.8
C
Call
$70
3.7
D
Put
$60
3.0
E
Put
$65
5.1
F
Put
$70
Explanation / Answer
delta of call = 0.70=N(d1)
delta of put=N(d1)-1=0.70-1=-0.30
chg in put price/chg in stock price=-0.30
=>chg in put price=-0.30*(chg in stock price)
=>chg in put price=-0.30*(63.2-64)
=>chg in put price=-0.30*(-0.80)=0.24
=>final mkt price=intial mkt price+0.24
=>final mkt price=3+0.24=3.24
Thus market price of Option D is $3.24 after the stock price changes to $63.2.
probability that the option will not be exercised on maturity date=N(-d2)=1-N(d2)
probability that the option will be exercised on maturity date=1-N(-d2)=1-(1-N(d2))=N(d2)=0.48
N(d1)=delta=0.56
By BSM price of option B=64*0.56-65*0.48*exp(-r*0.50)
let r=5% =>price of option B=64*0.56-65*0.48*exp(-0.05*0.50)=5.41 <5.8 hence the option is overpriced.
shares bought to hedge your position=0.56*100=56
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