Convexity

[Jolie]

1. The definition of convexity is it’s a non-linear change in price of a bond, given a change in yield. This does not indicate a side bias. However, higher convexity does mean a higher increase in price when rates go down and a lower decrease in price when rates go up. This is also what a positive convexity is. And vice versa for negative convexity. Can we then say that higher convexity = positive convexity and lower convexity =negative convexity?

2. Any more sources of convexity other than 1) lower coupon 2) An embedded or indirect call/put option ?

[125mph]

1. Sort of. You can also say lower convexity = selling convexity, and higher convexity = buying convexity

2. You only need to know that writing options lowers convexity and buying options increases convexity.

[S2000magician]

@Jolie

1. The definition of convexity is it’s a non-linear change in price of a bond, given a change in yield. This does not indicate a side bias. However, higher convexity does mean a higher increase in price when rates go down and a lower decrease in price when rates go up. This is also what a positive convexity is. And vice versa for negative convexity. Can we then say that higher convexity = positive convexity and lower convexity =negative convexity?

Convexity has a continuum from −∞ to +∞. So higher convexity can mean small negative vs. big negative, or zero vs. negative, or positive vs. negative, or positive vs. zero, or big positive vs. small positive. Conversely for lower convexity.

@Jolie

2. Any more sources of convexity other than 1) lower coupon 2) An embedded or indirect call/put option?

Increasing maturity adds (positive) convexity. Long positions in futures/forwards add convexity. Long positions in swaps add convexity.