Hopefully someone can help me out here with a “hypothetical problem.” I can’t seem to wrap my head around rounding in some of the practice problems.
In Vignette
Strike = $40, Stock = $40, Continuously compounded rate = 5.0%
The person “concludes” the 9-month put is mispriced relative to the 9-month call (Arbitrage is possible)
Person also “concludes” the 3-month put is correctly priced relative to its call option (No arbitrage)
Then a question asks you to test whether this person is right
A) Correct on both options
B) Correct on 3-month option
C) Correct on 9-month option
3-month (should be arbitrage free)
Call = $5.0 & Put = $4.5
9-month (should have arbitrage opportunity)
Call = $8.81 & Put = $7.34
After doing my calculations…
[3-month]
Synthetic Put = $4.5099 & Put = $4.50
Rounds to $4.51 so is this $0.01 difference meaningful or should I just assume the $4.5099 is ~ close enough to say there is no arbitrage?
[9-month]
Synthetic Put = $7.3576 & Put = $7.34
Rounds to $7.36 so there should be an arbitrage here then?
This may be nothing to worry about and the CFA institute may test these areas so the differences aren’t as close as these, but nonetheless some clarity on this would be helpful! Anyway, I’m sure someone here has run into this sort of problem before.
Thanks in advance for any help!
Side Note
I had a similar problem with swap rate calculations when I stored each PV factor and then summed my stored inputs which always gave me a slightly incorrect answer in the CFA practice problems (maybe 3.15% rate instead of 3.13% rate, small difference but meaningful in Notional values).
I realized they want you to basically write down 4 decimals places for each swap rate period (.9844 + .9500 + .8811, etc) and sum with less precision.
This sort of bothered me since storing these PV factors and summing them was both A) quicker to do on a calculator & B) more accurate than the way they desire you to make these calculations