1a. Describe two problems in using the Black option on futures pricing model for

Question

1a.   Describe two problems in using the Black option on futures pricing model for pricing options on Eurodollar futures.

1b.   Suppose someone offers you the following gamble: You pay $7 and toss a coin. If the coin comes up heads, he pays you $10, and if tails comes up, he pays you $5. You in turn get the idea of offering another person a coin toss in which he pays you $7 and tosses another coin. You tell him that if heads comes up, you will pay him $9, and if tails comes up, you will pay him $5. You think you see an opportunity to earn an arbitrage profit by engaging in both transactions at the same time. Why is this not an arbitrage opportunity? How could you make it one assuming that you could get two people to engage in these gambles?

Explanation / Answer

Ans 1 a: The major drawback with Black & Schole models is that it asks for usage of lognormal function, which infact returns with predetrmined/calculated rate but in real world there is huge deviation. secondly, It does not recognize the opportunity of arbitration.

Ans 1b:Arbitration is taking the advantage due to differences in prices at two locations, the aim of arbitration is buying in less and selling it in more thus making a profit. While in the situation given, it is purely a situation of probability whose outcome is not in your hand rather not is predicted, It is purely on luck. Hence this can not be termed as arbitration. In this gamble if we get two persons then we can analyse that If at first instance head comes with both persons then the gain is 1 for us, secondly lets assume in first even head comes and in second event tail comes then the profit will be 5, thirdly, in first event tail comes and in second event head comes then the loss is of 4 now assume tail comes in first gamble and tail comes in second gamble then there will not be any gain and any loss, so here to get two person we must offer the person in second gable lessor than 5 in both the flip of coins i.e. heads/tails, but that is highly unlikely.

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