Explain the term structure of yield volatility and how it influences the volatility of prices

Yield volatility typically varies by maturity. Short-term yields tend to be the most volatile because they respond directly to monetary policy and economic news, while long-term yields are anchored by expectations of average rates over many years. Price volatility, however, is roughly modified duration multiplied by yield volatility. A 30-year bond with duration near 17 and yield volatility of 60 basis points has far greater price risk than a two-year bond with duration near 2 and yield volatility of 95 basis points. The trap is to conclude that the most volatile yields produce the most volatile prices. Volatility structure also matters for pricing options embedded in bonds.