We consider a zero-coupon bond with a maturity of 10 years, face value of CHF 100 million and YTM of 10%.

Question:

1. Compute the price of the bond and its modified duration (sensitivity).

2. How does the price of the bond change when the YTM decreases to 9%? Compute the change by using the sensitivity and the direct price calculation and justify the differences.

3. Compute the convexity of the bond. Compute the change in the price of the bond when the YTM decreases to 9% while taking into account the convexity. Compare your results to the ones in question and justify the differences.