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Homework answers / question archive / Strike 50 Call premium =9 The premium has two components :

Strike 50 Call premium =9 The premium has two components :

Finance

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

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