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For my own knowledge, i think the price of the bond can be found by using the spot rates, also there is no cash flow in the modified convexity since this is the course about mathematical finance. Thank you!

2 years The following table shows the information of 2 bonds. Bond term Face value Annual Coupon rate (Frequency) Bond A 100 3% (Semi-annual) Bond B 3 years 100 4% (Annual) (*Note: The yield rates are quoted as annual effective yield rate) On the other hand, the current spot rates of various maturities are given in the table below. Term 6 months 12 months 18 months 24 months 30 months 36 months (0.5 year) (1.5 years) (2 years) (2.5 years) (3 years) Spot rate 2% 2% 2.2% 2.3% 2.3% 2.5% (*Note: All spot rates are quoted as annual effective interest rate) 1 year Questions (a) We first consider the bond A. (i) Calculate the annual effective yield rate of the bond A. (ii) Hence, calculate the modified duration and modified convexity of bond A. (b) Suppose that the spot rates after 6 months are decreased uniformly by 0.2%, calculate the annual effective yield rate of the bond B at that time. (Note: In finding the yield rate, you need to present the governing equation (with explanation) of the yield rate. However, you don't need to show the calculation on how to solve those equations.) 2 years The following table shows the information of 2 bonds. Bond term Face value Annual Coupon rate (Frequency) Bond A 100 3% (Semi-annual) Bond B 3 years 100 4% (Annual) (*Note: The yield rates are quoted as annual effective yield rate) On the other hand, the current spot rates of various maturities are given in the table below. Term 6 months 12 months 18 months 24 months 30 months 36 months (0.5 year) (1.5 years) (2 years) (2.5 years) (3 years) Spot rate 2% 2% 2.2% 2.3% 2.3% 2.5% (*Note: All spot rates are quoted as annual effective interest rate) 1 year Questions (a) We first consider the bond A. (i) Calculate the annual effective yield rate of the bond A. (ii) Hence, calculate the modified duration and modified convexity of bond A. (b) Suppose that the spot rates after 6 months are decreased uniformly by 0.2%, calculate the annual effective yield rate of the bond B at that time. (Note: In finding the yield rate, you need to present the governing equation (with explanation) of the yield rate. However, you don't need to show the calculation on how to solve those equations.)

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