# Forward contract after initiation - no arbitrage price

Hi all,

Can anybody help explaining Practice Problem question 7 of the Curriculum, reading 39?

Calculating no-arbitrage price 3 months after initiation. The explanation for the problem says F0.25(T)=[(245+0-1.5)/(1+0,00325)(0.5-0.25)] * (1+0,00325)(0.75-0.25).

Why is the first part (245+0-1.5) discounted by (1+0,00325)(0.5-0.25)?

Thanks for any hints, derivatives are hell I’m struggling with the exam value vs the difficulty of this a lot Petr

Derivatives suck. Here is how I did this problem. Not sure if it matches up to the curriculum but I will try and explain it as simply as I can. Which will still be complicated because these problems take so long.

The first step with these problems is to try and get everything in the same time period.

You have to compare the forward price at initiation with the new updated forward price. The forward price at initiation is 250.562289 – they gave this in the problem and this won’t change. The updated forward price is going to be the stock price of 250 grown at the risk free rate of .325% for 6 months (because the contract was for 9 months, and 3 months have passed). So to find that you do 250* (1+.325%)(6/12). You also need to account for the fact that the company issues a dividend, which will reduce the future stock value by the amount of the dividend. The dividend is going to be issued 3 months before the contract expires, so at expiration it will be worth 1.50*(1+.325%)(3/12). So the updated stock value at expiration will be (Stock – Dividend) = 243.8966.

So now you have the original forward value at expiration of 250.5623 vs the new value of 243.8966. Remember, these are values at expiration, which is 6 months from today. The problem asks for the value today so you need to find the difference (250.5623-243.8966) and discount this 6 months back. So you discount by (1+.325%)(6/12). And that’s your answer.

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Thank you for pointing out the dividend!! Another stupid mistake on my part. I missed that only the dividend is discounted, not the whole thing in the parentheses…