Hi I am an accounting professional that works at an insurance firm. We hold many types of securities$,$ one of them being Middle Market Loans. $($we call them Bank Loans$)$ We primarily purchase all of these securities at a discount where the average price is ~$$98\mathrm{.}50.$ My current understanding on book value is that when bought at a discount the book value will accrete up to it$$s face value throughout the life of the security such that at maturity the BV$=$Par. My basic question is whether given this scenario, can the book value of the security held ever exceed the face value of the bond?

To add more color and complexity, these securities are often floating rate securities $($so base rates like LIBOR$/$SOFR $+$ basis points$)$ and the payment schedule and terms can continuously change per borrower. $($like quarterly reset and coupon to monthly, ect. Which prompts a new cash flow $$tier$$ or period going forward$)$ Furthermore, we use the prospective book value calculation for these securities where the cost and yield are being continuously recalculated. $($That$$s my understanding of the prospective method but correct me if I am wrong$)$ Given these new details, does that change the answer to my original question? Can a bonds book value exceed the bond$$s face when it was originally bought at a discount? I think some of my confusion lies in what factors in the BV calculation are affected by rising rates and schedule changes. Like a higher rate will cause cash flows projected out to be higher which leads to a higher yield needed to discount those cash flows back...but how does BV fit in$?$ Hopefully you can help! Thanks!!