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Provide an intuitive explanation for the nature of the volatility risk of callable and puttable bonds,...

Provide an intuitive explanation for the nature of the volatility risk of callable and puttable bonds, which is that interest rate volatility has a negative relation with the price of a callable bond, but a positive relation with the price of a puttable bond.

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In callable bond the issuer has right to call back the bond at the pre-determined price fixed at the time of issue. On the other hand , in case of puttable bond the investor has the right to sale the bond at the pre-determined price fixed at the time of issue.

Interest rate volatility means the risk of change in the interest rate.

Negative relation of Interest rate volatility on price of callable bond

As discussed above the issuer has the right to call back the bond. In case the interest rate falls the issuer can opt for bond refinancing option. Hence higher the interest rate volatility the price of the bond will be at greater discount to compensate the call option and vice versa.

Positive relation of Interest rate volatility on price of puttable bond

As discussed above the investor has the right to sell back the bond. In case the interest rate rises the investor can sale the bond at pre determined price and invest in cheaper bond. Hence higher the volatility of the interest rate is favourable for investor so the price will be at premium and vice versa.

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