Yes jairam. Lets consider these: all options have 1 month to maturity with the same underlying with the current price of underlying of 50.16. The prices of
(these are the traded prices and options i have picked up from the internet)
Buy 1 ITM Call: X=45,price=5.15
Sell 1 OTM Call:X=55,price=.14
Buy 1 ITM Put:X=55,price=3.45
Sell 1 OTM Put:X=45,price=.35
Thus we establish the box position at price of -5.15+.14-3.45+.35=-8.11 that is cost of $ 8.11 we establish the position.
Lets say after 1 month the stock price is ST therefore payoffs of all the options:
Buy 1 ITM Call: max(ST-45,0)
Sell 1 OTM Call:-max(ST-55,0)
Buy 1 ITM Put:max(55-ST,0)
Sell 1 OTM Put:-max(45-ST,0) so that the net payoff at the end of 1 month=max(ST-45,0)-max(ST-55,0)+max(55-ST,0)-max(45-ST,0)
suppose that after 1 month ST<45 so that net payoff at the end of 1 month=0-0+55-ST-(45-ST)=10
suppose that after 1 month 55>ST>45 so that net payoff at the end of 1 month=ST-45-0+55-ST-0=10
suppose that after 1 month ST>55 so that net payoff at the end of 1 month=ST-45-(ST-55)=10
therefore the net payoff after the 1 month period is the same at $10 whatever the asset price.Thus the return is the same risk-less $10 at the maturity.
The Present value of $10=$10*exp(-10%*1/12)=$9.11
therefore we have made a risk less profit of $9.11-8.11=$1 in present value terms.
The return earned is exactly not risk less because i have taken the actual practical traded prices and that the transaction costs are also not considered.
thanks
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