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Strike 50 Call premium =9 The premium has two components :
Strike 50 Call premium =9
The premium has two components :
.1 Intrinsic Value
.2 Time Value
The buyer has the right to BUY at 50
If the spot Price is say, 55
The buyer will make gain of 5 if he can immediately exercise his right to buy .
He will buy at 50 and sell at 55.
Hence , the intrinsic value of the call option will be 5 and remaining 4 will be time value
For a given expiry , the Intrinsic value is constant , the premium varies with strike price based on the intrinsic value
If strike 50 has a premium =9,
Strike 55 should have a lower premium.
If spot price is 55, the intrinsic value is Nil and the premium should be =4
In this case the premium is 10, which gives rise to arbitrage opportunity.
ARBITRAGE STRATEGY:
BUY CALL at Strike 50
SELL CALL at strike 55
Net Cash inflow =-9+10=1
Assume price at expiration =S
Payoff for BUY call option Strike 50=Max.(S-50),0)
Payoff for SELL call option Strike 55=Min.(55-S),0)
The Payoffs and Net profit at different Expiration Price is given below:
It may be noted that there will always be an arbitrage profit
|
S |
A |
B |
C=A+B+1 |
|
Price at expiration |
Payoff BUY Call Strike 50 |
Payoff SELL Call Strike 55 |
Net Profit |
|
47 |
0 |
0 |
1 |
|
48 |
0 |
0 |
1 |
|
49 |
0 |
0 |
1 |
|
50 |
0 |
0 |
1 |
|
51 |
1 |
0 |
2 |
|
52 |
2 |
0 |
3 |
|
53 |
3 |
0 |
4 |
|
54 |
4 |
0 |
5 |
|
55 |
5 |
0 |
6 |
|
56 |
6 |
-1 |
6 |
|
57 |
7 |
-2 |
6 |
|
58 |
8 |
-3 |
6 |
|
59 |
9 |
-4 |
6 |
|
60 |
10 |
-5 |
6 |
PUT OPTION:
Put option with strike=50
The buyer has the right to SELL at 50
If the spot Price is say, 47
The buyer will make gain of 3 if he can immediately exercise his right to buy .
He will buy at 47 and sell at 50.
Hence , the intrinsic value of the Put option will be 3 and remaining 4 will be time value
For a given expiry , the Intrinsic value is constant , the premium varies with strike price based on the intrinsic value
If strike 50 has a premium =7,
Strike 55 should have a higher premium.
If spot price is 45, the intrinsic value is 10 and the premium should be =10+4=14
In this case the premium is 6, which gives rise to arbitrage opportunity.
ARBITRAGE STRATEGY:
BUY Put at Strike 55
SELL PUt at strike 50
Net Cash inflow =-6+7=1
Assume price at expiration =S
Payoff for BUY Put option Strike 55=Max.(55-S),0)
Payoff for SELL Put option Strike 50=Min.(S-50),0)
The Payoffs and Net profit at different Expiration Price is given below:
It may be noted that there will always be an arbitrage profit
|
S |
A |
B |
C=A+B+1 |
|
Price at expiration |
Payoff BUY Put Strike 55 |
Payoff SELL Put Strike 50 |
Net Profit |
|
47 |
8 |
-3 |
6 |
|
48 |
7 |
-2 |
6 |
|
49 |
6 |
-1 |
6 |
|
50 |
5 |
0 |
6 |
|
51 |
4 |
0 |
5 |
|
52 |
3 |
0 |
4 |
|
53 |
2 |
0 |
3 |
|
54 |
1 |
0 |
2 |
|
55 |
0 |
0 |
1 |
|
56 |
0 |
0 |
1 |
|
57 |
0 |
0 |
1 |
|
58 |
0 |
0 |
1 |
|
59 |
0 |
0 |
1 |
|
60 |
0 |
0 |
1 |
Expert Solution
Strike 50 Call premium =16
The premium has two components :
.1 Intrinsic Value
.2 Time Value
The buyer has the right to BUY at 50
If the spot Price is say, 60
The buyer will make gain of 10 if he can immediately exercise his right to buy .
He will buy at 50 and sell at 60.
Hence , the intrinsic value of the call option will be 10 and remaining 6 will be time value
For a given expiry , the Intrinsic value is constant , the premium varies with strike price based on the intrinsic value
If strike 50 has a premium =16,
Strike 55 should have a lower premium.
If spot price is 60, the intrinsic value is 5 and the premium should be =5+6=11
In this case the premium is 10, which gives rise to arbitrage opportunity.
ARBITRAGE STRATEGY:
SELL CALL at Strike 50
BUY CALL at strike 55
Net Cash outflow =16-10=6
Assume price at expiration =S
Payoff for SELL call option Strike 50=Min.((50-S),0)
Payoff for BUY call option Strike 55=Max.((S-55),0)
The Payoffs and Net profit at different Expiration Price is given below:
It may be noted that there will always be an arbitrage profit(Minimum profit=1)
|
S |
A |
B |
C=A+B+6 |
|
Price at expiration |
Payoff SELL Call Strike 50 |
Payoff BUY Call Strike 55 |
Net Profit |
|
47 |
0 |
0 |
6 |
|
48 |
0 |
0 |
6 |
|
49 |
0 |
0 |
6 |
|
50 |
0 |
0 |
6 |
|
51 |
-1 |
0 |
5 |
|
52 |
-2 |
0 |
4 |
|
53 |
-3 |
0 |
3 |
|
54 |
-4 |
0 |
2 |
|
55 |
-5 |
0 |
1 |
|
56 |
-6 |
1 |
1 |
|
57 |
-7 |
2 |
1 |
|
58 |
-8 |
3 |
1 |
|
59 |
-9 |
4 |
1 |
|
60 |
-10 |
5 |
1 |
PUT OPTION:
Put option with strike=50
The buyer has the right to SELL at 50
If the spot Price is say, 47
The buyer will make gain of 3 if he can immediately exercise his right to buy .
He will buy at 47 and sell at 50.
Hence , the intrinsic value of the Put option will be 3 and remaining 4 will be time value
For a given expiry , the Intrinsic value is constant , the premium varies with strike price based on the intrinsic value
If strike 50 has a premium =7,
Strike 55 should have a higher premium at 7+(55-50)=12
In this case the premium is 14, which gives rise to arbitrage opportunity.
ARBITRAGE STRATEGY:
BUY Put at Strike 50
SELL PUt at strike 55
Net Cash inflow =-7+14=7
Assume price at expiration =S
Payoff for BUY Put option Strike 50=Max.(50-S),0)
Payoff for SELL Put option Strike 55=Min.(S-55),0)
The Payoffs and Net profit at different Expiration Price is given below:
It may be noted that there will always be an arbitrage profit(Minimum Profit=2)
|
S |
A |
B |
C=A+B+7 |
|
Price at expiration |
Payoff SELL Put Strike 55 |
Payoff BUY Put Strike 50 |
Net Profit |
|
47 |
-8 |
3 |
2 |
|
48 |
-7 |
2 |
2 |
|
49 |
-6 |
1 |
2 |
|
50 |
-5 |
0 |
2 |
|
51 |
-4 |
0 |
3 |
|
52 |
-3 |
0 |
4 |
|
53 |
-2 |
0 |
5 |
|
54 |
-1 |
0 |
6 |
|
55 |
0 |
0 |
7 |
|
56 |
0 |
0 |
7 |
|
57 |
0 |
0 |
7 |
|
58 |
0 |
0 |
7 |
|
59 |
0 |
0 |
7 |
|
60 |
0 |
0 |
7 |
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