You have just opened the morning newspaper to check the prices of call options o
ID: 2818202 • Letter: Y
Question
You have just opened the morning newspaper to check the prices of call options on asset ABC. It is now December, with the near contract maturing in one month's time. Asset ABC is currently trading at $50. Strike Jan. Mar. June $40 $11 $12 $11.50 8.50 9.00 50 7 60 Glancing at the figures, you note that two of these quotes seem to violate some of the rules you learned regarding option pricing. What are these discrepancies? How could you take advantage of the discrepancies? What is the minimum profit you would realize by arbitraging based on these discrepancies? a. b. c. Suppose the price of the January $40 call was $9 rather than $11. The option would thus be selling for less than its intrinsic value. Why might it not be the case that an arbitrage profit is instantly available?Explanation / Answer
Hi,
a) The price of an option has two components, intrinsic value and the time value of money
If we look at the premiums for strike 40 option for March and June we will know that:
The intrinsic value of the option for both is (50-40), that is $ 10
however the extrinsic value is decreasing over the period, as we all know that assuming positive interest rates, money will only inflate in future and hence the price for March option cannot be larger than the June option. There seems to be a problem here which can be taken advantage of
b) We can easily make money if we are long on the June Option, that means we pay ($-11.5) and we are short March option, that is we get ($12), in effect we will make $0.5 for every pair of such a strategy option
c) If the January option prices are trading at $9, the arbitrage profit would only be available when the market realises that there is something wrong in the prices and then it tries to get back to the stage where there is no arbitrage, that is the point when we can sell that option for more premium. Therefore, the profit is not immediate nut it is definitely certain
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