Thiruspace.com : SampleTopics : Bond Convexity 4.3.9
Duration and Convexity - Some Interesting Calculations..
Bond Price Behaviour - First lessons in Convexity.
Simply put Duration is the weighted maturity of a bond's cash flows:
Sum(C
t *t*(1/(1+r)^t)) / Sum(C
t*(1/(1+r)^t))
where C
t is cash flow in period t and r is the interest rate.
As you can see in the following chart, considering Duration, by itself, leads to an incomplete picture of a typical risk-profile, as it renders merely the
linear coefficient of changes in market-curve.
Convexity is the second-degree expansion of Taylor Series (that we discussed in
a previous session). The sum of both Duration and Convexity numbers,
calculates an effective Price for a Bond at a given yield point. This effective
price computation should be reasonably closer to Actual price computation.
Bond Price Behaviour -> Duration + Convexity Effect