Question: Answer the following questions related to the case study "Convexity of long bonds, convexity and arbitrage."

a. First the preliminaries. Explain what is meant by convexity of long-dated bonds.

b. What is meant by the convexity of long-dated interest rate swaps?

c. Explain the notion of convexity using a graph.

d. If bonds are convex, which fixed-income instrument is not convex?

e. Describe the cash flows of FRAs. When are FRAs settled in the market?

f. What is the convexity adjustment for FRAs?

g. What is a cap? What volatility do you buy or sell using caps?

h. Now the real issue. Explain the position taken by "knowledgeable" professionals.

i. In particular, is this a position on the direction of rates or something else? In fact, can you explain why the professionals had to hedge their position using caps or floors?

j. Do they have to hedge using caps only? Can floors do as well? Explain your answer graphically.

k. Is this a true arbitrage? Are there any risks?