The issuer can call the bond back when rates fall. Drag the yield and watch the call cap the price, bend the curve the wrong way and set the date the bond is redeemed.
A callable bond lets the issuer redeem it early at a fixed call price. Investors are short that option, so when rates fall the price stops near the call price instead of rising with the straight bond. This lab prices the call, shows where convexity turns negative, compares yield to maturity with yield to worst, and marks the dates on which the issuer would call.
The price–yield curve bends the wrong way: as yields fall the price rises ever more slowly because a call becomes likelier, so a fall in yield helps less than a rise hurts. The lab measures it as effective convexity, from prices at ±25 bp.
The lowest yield an investor can earn over maturity and every possible call date. For a bond trading above the call price it is usually the yield to the first call, which is why yield to maturity overstates the return.
When refinancing is cheaper than the coupons: if the remaining bond is worth more than the call price at the current yield, the issuer gains by redeeming. The timeline marks each call date this way and highlights the first one.
Duration measured from the actual price change when the whole yield curve moves by a small amount, here 25 bp each way. It is needed because the cash flows of a callable bond change with yields, so the usual duration formula does not apply.