A non-callable 3-year UK government bond pays semi-annual coupons. The face value is $10,000, the annual coupon rate is 2% and the annual yield to maturity is 14% per year. (a) Show clearly how the annual modified duration is calculated from the data above and explain how the modified duration can be used to estimate a price change resulting from a change in yield. (5 marks) (b) The convexity of the bond in part (a) is 8.81. Explain what is meant by convexity with regard to the price-yield relationship and how it helps improve the price change estimate you calculated in part (b). Use graphs where appropriate. (10 marks) (c) Does the level of the initial yield influence the duration of a bond? If so, explain this. Use graphs where appropriate. (5 marks) (d) The terms 'negative convexity' and 'price compression' are often used when discussing callable bonds. Explain these terms and the term 'callable' bond. Use graphs where appropriate. (10 marks)