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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 |