Fixed income management

Can someone please explain how the purchase of a call option can protect against a decline in reinvestment rates resulting from a drop in interest rate . Also how does selling a put provides protection when rates are on the increase?

Investor sold the call option to the callable bond issuer so that bond issuer has a right to call the bond and refinace at lower I/R when I/R decreses. The value of call option increaes so that the value of the bond will not increase as much as option-free bond when I/R decreses which is unfavorable to the Investor. Investor can buy a call option to offset the call option sold to the bond issuer and the net total value will be same as that of option-free bond. A put is valuable when I/R increses because I/R increses means decrease of bond price and the bond can be sold at put strike price if I/R increses. Hope this will be helpful.

You have to understand what is the underlining. In this case, the underlying is bond or bond future. So if rates decrease (so reinvestment rates fall), the price of the bond rise and the call will pay off, hence providing protection from lower reinvestment rates.