# Derivatives Topic Test Parisi

Hey everyone,

in question 2 of Derivatives Topic Test Parisi we are supposed to determine if there is a possibility for arbitrage. In order to do so, in the answer they compute the value of the contract at the current time, but isn’t that the formula for the price??

The rest of the answer also seems to indicate that the just confused value with price because we find out that the price/value is higher than today spot price of the underlying and thus conclude we can make a profit by buying the underlying today and selling the forward contract.

Could someone help here?

Thanks,

Tartaglia

Also the answer switches back and forth between calling the contract a forward and a future…

And, I am not sure how that arbitrage profit of of 4.84 is computed.

I would greatly appreciate some help on this one.

You need to find the new price of the contract given the current index. Then Take the difference. In the answer, they are calculating the price, not the value

Ok, I agree. They make multiple mistakes in my opinion (or maybe I am making a mistake here)>

1. Confuse Forward and Future. The Forward contract price is set at the beginning and does not change over the life of the contract, only the value does. The price of a future on the other changes daily in the process of the mark to market and converges towards the price of the underlying at time T.

2. As you confirmed, the confuse price and value.

3. The difference is 1.72 not 4.84.

Can you confirm this?

Also, should we discount the difference between the buying price and the selling price to today’s value, since the profit cannot be realized until 30 days from now?

I can confirm that the diff is 4.84 as stated. How do you get 1.72? And why do you discount it? You need to find the 30 days forward price. Then, take the difference

You are right, I mixed up numbers and concepts slightly regarding the difference and the discounting.

But I am still confused about their use of language. With a forward contract the price does not change, but is negotiated at the beginning when the contract is agreed upon.

When they are computing the price (and calling it the value) in the solution, they are computing the hypothetical no-arbitrage price that would be necessary to make sure that the value of the contract would 0. Given that the price they come up with is different than the actual price of the forward, we then have an arbitrage opportunity, correct?

So the only mistake is that they call the price the value in the question and in the answer?