Adding Convexity with options
I understand when we add convexity we:
The bond with higher convexity will have higher price than the one with lower convexity. In a volatile market, this is beneficial and we want to add convexity.
An example, is adding convexity by Buying a call option on a bond.
If interest rates decrease –> we’re in better shape than the straight bond –>because we can call –> Higher price using the higher convexity option.
If interest rates increase –> How is that this same higher convexity bond has a higher price than the straight bond? I just see it as the options being worth nothing and approaches the same price as straight. More specifically what they get at is they say total performance of the portfolio with options is greater than portfolio without options. Why in rising environment would total performance be greater? I think it would just match the portfolio with options because the option is worthless.