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

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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