This question asks to develop three mini-essays on pricing and hedging in fixed income markets. (i) (10 points) The par rate or for a given maturity T is the coupon rate that makes a T-year coupon bond sell for par. Describe the relation between swap rates, zero-coupon bonds and par rates. (ii) (15 points) Explain how the asset-liability management of instruments with neg- ative convexity may lead to an increased volatility of interest rates. (iii) (15 points) Provide two examples of mortgage-backed securities. Discuss their pricing as well as their risk profile, i.e. how the value of the security varies when interest rates increase (or decrease).