问题如下:
Suppose an investor expects that the 1-year rate will remain at 6% for the first year for a 2-year zero-coupon bond. The investor also projects a 50% probability that the 1-year spot rate will be 8% in one year and a 50% probability that the 1-year spot rate will be 4% in one year. Which of the following inequalities most accurately reflects the convexity effect for this 2-year bond using Jensen’s inequality formula?
选项:
A. $0.89031 > $0.89000.
B. $0.89000 > $0.80000.
C. $0.94340 > $0.89031.
D. $0.94373 > $0.94340
解释:
The left-hand side of Jensen’s inequality is the expected price in one year using the 1-year spot rates of 8% and 4%
The expected price in one year using an expected rate of 6% computes the right-hand side of the inequality as:
Next, divide each side of the equation by 1.06 to discount the expected 1-year zero-coupon bond price for one more year at 6%. The price of the 2-year zero-coupon bond equals $0.89031 (calculated as $0.94373 / 1.06), which is greater than $0.89000 (the price of a 2-year zero-coupon bond discounted for two years at the expected rate of 6%). Thus, Jensen’s inequality reveals that $0.89031 > $0.89000
题目能做正确,但是我是算除了0.89031这个书,再联想convexy涨多跌少的性质会使得实际债权价格更大才选正确A的,讲课的时候有提到Jensen’s ineuality这个知识点么?似乎没有印象了,如果讲义上有,麻烦告知一下在那一页,谢谢!