Effective Convexity (Numerical)
Computes the effective convexity of a bond by finite differences, repricing the instrument for an up and a down yield move: (V− + V+ − 2·V0)/(V0·Δy²). Unlike analytical convexity, the effective version works even for bonds with uncertain cash flows, such as those with embedded options, because it only needs the three prices. It complements duration to better estimate the price change in large rate moves. Enter the three prices and the yield change used.
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Effective Convexity (Numerical)
Computes the effective convexity of a bond by finite differences, repricing the instrument for an up and a down yield move: (V− + V+ − 2·V0)/(V0·Δy²). Unlike analytical convexity, the effective version works even for bonds with uncertain cash flows, such as those with embedded options, because it only needs the three prices. It complements duration to better estimate the price change in large rate moves. Enter the three prices and the yield change used.
When duration alone falls short
Duration estimates how much a bond's price changes when rates move, but it works with a straight line, and the price-yield relationship is curved. For small moves the line is fine; for big ones it misses, and that's where convexity comes in. The effective version computes that curvature the hard way, by repricing the bond for a rate rise and a rate fall.
The big advantage of the numerical approach is that it works where the analytical formula fails. Bonds with embedded options, like callables, have cash flows that change with rates, and that breaks the closed-form formulas. Since effective convexity only needs three prices, it sidesteps the problem: you just need to know what the bond is worth today, with a slightly higher rate and with a slightly lower one.
Enter the base price, the price if the yield falls, the price if the yield rises and the yield change used on both sides. The tool returns the effective convexity, which you add to the duration estimate to better predict the price change in large rate shocks. Use the same shock magnitude on both sides, or the calculation goes off.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.