You are given the price of three different European puts on a stock S. The time

Question

You are given the price of three different European puts on a stock S. The time to expiration of the puts is 1 year, and the risk free interest rate is 8% compounded continuously. The prices of the puts follow. Identify two distinct arbitrage opportunities that are not scalar multiples of one another. You purchase an Asian option on the same underlying asset. The price of the asset in three, six, nine, twelve, fifteen, and eighteen months is 105, 110, 112, 107, 111, and 115: respectively. Determine the payoff of the following: a) a geometric average price Asian call with strike 106, b) an arithmetic average strike Asian call, c) an arithmetic average price Asian put with strike 120, d) and a geometric average strike Asian put.

Explanation / Answer

4.3)

Lets compare strike 30 and strike 32 puts
Difference = 2
Discounted value of difference= 1.85

Difference in value of put= 1.91

Hence 32 put can be said to be relatively overpriced
Sell 32 put and buy 30 put


Similarily if we take 30 put and 36 put:
Difference in strike =6
PV of difference in strike= 5.54
Difference in put price =5

hence 36 put is relatively underpriced

Hence buy 36 put and sell 30 put

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