I’ve been having trouble understanding convexity conceptually, but I think I might be starting to understand it.
- When rates are low (call is in the money), callable bonds have negative convexity because the call option essentially caps the bond’s price and, therefore, the bond is less sensitive to changes in interest rates.
- Putable bonds exhibit positive convexity at all times, like straight bonds, but, when rates are high (put is in the money), they exhibit “less positive” convexity compared to straight bonds because the put option floors the bond’s price, and, therefore, the putable bond is less sensitive to further changes in rates. When rates are high, a callable bond’s convexity will be positive and similar to the straight bond’s, because the call option is out of the money, and the bond otherwise lacks the downside protection that limits the downside potential of the putable bond, making it sensitive to interest rate changes.
Can someone confirm the above points? It helps me to type it out like this, so I appreciate it.
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