A company issues a 5-year step-up note paying semi-annual coupons. The coupon rate starts at 1.75% and goes up by 25 bps every year. The issue sells at $93.25 (par value is $100).

(a) What is the YTM (BEY basis) of this note?

(b) Use a 20 bps rate shock to estimate the duration and the convexity of the note.

(c) For yields in the range [0% ; 8%] with a step of 0.1%, draw the estimation error of the note price using duration only and duration & convexity (with respect to the exact price change), on the same graph.