This is probably going to sound like a dumb question but, say you have bonds with 10% coupon payments and face value we know is 1,000. If the bond is currently trading at 1,400 (a premium to the par value) why can you not just purchase the bond before a coupon payment, receive the coupon payment, and then sell the bond soon afterwards?
You can, but you probably won't make money on it.
When you buy a bond, the amount you actually pay is called the dirty price. However, the price quoted for a bond is usually the clean price, which is the dirty price minus the amount of interest which has accrued since the last coupon payment.
So, in your example, let's assume that coupons are paid annually, the amount of the coupon is $100, and the next coupon payment is a week from now (about 2% of a year). If you want to buy this bond, it will probably cost $1,498—that's the "dirty price." However, when you look at quotes for this bond, they'll probably show you the clean price instead. To calculate the clean price, subtract the accrued interest (in this case, $98) from the dirty price. The result is $1,400.
So, you buy this bond for $1,498 and wait for the coupon payment of $100. After the coupon payment, the clean price of the bond will probably stay around $1,400, but now the accrued interest is $0, so the dirty price of this bond is now $1,400.
All in all, you bought a bond for $1,498, and now you have a bond worth $1,400, as well as $100 cash. That's a gain of $2.
There's some worse news, though. Since the bond market is not very liquid, if you want to sell this bond, you'll probably get significantly less than the asking price. Maybe you'll get $1,375 instead of $1,400. The bottom line is that you have a loss of $23.