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KIC000057 - Convexity Matters We can approximate the change...

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Unformatted text preview: Convexity Matters - We can approximate the change in price relative to the change In yield with what‘s called a Taylor series expansion. - Taylor series can be expressed with several terms or orders, depending on how well the approximation works relative to the function we are talking about. - If we want to worry about convexity, then we can use a 2"“ order expansion and see how price changes relative to the change of change (second derivative). dP = %dy+ £3 (rily)z + error More Problems with Duration What did we learn about the last two lectures? What are we implicitly assuming when we wiculate duration? . We start with a flawed assumption about pricing and discount rates => we would rather discount cash flows at different rates When we take the derivative, we are assuming the yield curve is flat and all shifts are parallel in nature. Another concern is that for bonds with embedded options, we need to worry about how the option value impacts price changes. ‘, ‘ Convexity Matters - Change in price approximation: dP 1 (PP 511’ = Edy +5301!”2 + error error P . 2 all” dPld +ig—fi(dy)2+ Zdy P ...
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