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

###### Finance

The premium has two components :

.1 Intrinsic Value

.2 Time Value

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:

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:

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

## 2.91 USD

### Option 2

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