USE THE INFORMATION GIVEN BELOW TO ANSWER QUESTIONS 1-2. The Wall Street Journal
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Question
USE THE INFORMATION GIVEN BELOW TO ANSWER QUESTIONS 1-2.
The Wall Street Journal reported the following prices for Microsoft options for trading on Friday, February 7 2010. The stock itself closed at $50.75.
Calls (Prices in $)
Strike Price
February
March
April
July
45
6.625
7.5
8
10.5
50
2.8125
4.75
5.875
55
1.0625
2.625
3.75
6
60
0.4375
1.3125
1.875
4.25
65
0.1875
0.625
1.25
70
0.0625
Puts (Prices in $)
Strike Price
February
March
April
July
45
1
1.8125
2.625
4.25
50
2.375
4
5
55
5.375
7.625
8.125
8.75
60
9.75
10.875
12.5
65
15.5
16.5
16.75
70
20.75
1) If the risk free rate of interest (continuously compounded) is 5%, then does put- call parity hold for the April options with X=K=$50, and X=K=$65 (calculations based on 71 days to maturity, 365 day year)?
2a) Construct a payoff diagram for buying a $50 April call option on Microsoft. Construct the diagrams for net payoffs, i. e. after deducting the option premium.
2b) Construct a payoff diagram for writing a $50 April call option on Microsoft and for writing a $50 April put option (combined). Construct the diagrams for net payoffs, i. e. after adding the option premium.
Calls (Prices in $)
Strike Price
February
March
April
July
45
6.625
7.5
8
10.5
50
2.8125
4.75
5.875
55
1.0625
2.625
3.75
6
60
0.4375
1.3125
1.875
4.25
65
0.1875
0.625
1.25
70
0.0625
Puts (Prices in $)
Strike Price
February
March
April
July
45
1
1.8125
2.625
4.25
50
2.375
4
5
55
5.375
7.625
8.125
8.75
60
9.75
10.875
12.5
65
15.5
16.5
16.75
70
20.75
Explanation / Answer
1 As per put call parity we have P=C -S + Xe^-rt For X=K=50 we have; Risk free rate 5% Call price is 5.875 April option Stock price 50.75 Strike price 50 Maturity 71 days As per put call parity Put price is 4.642344663 As per table the put price is 5 so thre is arbitrage opportunity For X=K=65 we have; Risk free rate 5% Call price is 1.25 April option Stock price 50.75 Strike price 65 Maturity 71 days As per put call parity Put price is 14.87254806 As per table the put price is 16.75 so there is arbitrage opportunity 2a.For a call with strike of 50 will start making profit after stock price rises above 55.875 as 5.875 is option premium Strike Stock price Payoff 50 50 -5.875 50 51 -4.875 50 52 -3.875 50 53 -2.875 50 54 -1.875 50 55 -0.875 50 56 0.125 50 57 1.125 50 58 2.125 50 59 3.125 50 60 4.125 50 61 5.125 till infinity 2b.For writing a call with strike of 50 will start making loss after stock price rises above 55.875,it will be opposite of above as 5.875 is option premium Strike Stock price Payoff 50 50 5.875 50 51 4.875 50 52 3.875 50 53 2.875 50 54 1.875 50 55 0.875 50 56 -0.125 50 57 -1.125 50 58 -2.125 50 59 -3.125 50 60 -4.125 50 61 -5.125 till infinity For writing a put of strike 50 the payoff will be Premium is 16.75 Strike Stock price Payoff 50 50 16.75 50 49 15.75 50 48 14.75 50 47 13.75 50 46 12.75 50 45 11.75 50 44 10.75 50 43 9.75 50 42 8.75 50 41 7.75 50 40 6.75 50 39 5.75 50 38 4.75 50 37 3.75 50 36 2.75 50 35 1.75 50 34 0.75 50 33 -0.25 50 32 -1.25 50 31 -2.25
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