# Error from rounding

I just finish the first Schweser mock. i found a problem concerning the calculator decimal that I want to have your opinion.

In the question 101 PM mock 1, given Call = 8.81, Put = 7.34, S =K = 40, T = 0.75 (9 months) and r = 5%, is an arbitrage opportunity possible?

My answer is: the price of Put must be: Put = Call-S+K*exp(-0.05*0.75) = 8.81 - 40 + 40* exp(-0.05*0.75) = 7.33776709

Because 7.33776709 is different to 7.34, there is an arbitrage opportunity.

But the solution makes me surprise, schweser use same formula as mine but takes only 2 decimal digits and the price of Put is Put = 8.81 - 40 + 40* exp(-0.05*0.75) = 7.34 and so, there is no arbitrage opportunity.

Why two digits, but not three, four, or zero?

Do you have any suggestion to do if we get this kind of question in exam?

there’s also a similar problem in one of the Fixed Income Topic Tests. with 2 decimal places, there’s no arbitrage, but if you use 6 decimal places, there’s a 0.02 price difference.

this is why I asked for the proper number of decimals to use for the exam here, I’d probably go with CFAI Topic Test in this one and go 6 decimal places.

I totally agree with you.

Besides, the problem I mentionned seems more complex.

In my opinion, if the interest rate is different to zero, the CORRECT answer for this kind of question (is an arbitrage opportunity possible) is always YES.

Why? Because if r is different to zero, the terme exp(r*T) is NEVER a rational number. So, the Call-Put parity equation, with input given by CFAI, will be always invalid (even you take 6 or 100 digits). Without calculator, you can confirm: there is an arbitrage opportunity.