Short Rate Dollar Duration Lecture

Short Rate Dollar Duration Lecture - Debt Instruments and...

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Debt Instruments and Markets Professor Carpenter SR Duration and Hedging 1 Short Rate Dollar Duration, Duration, and Hedging Duration and dollar duration indicate how sensitive a bond is to changes in interest rates and can be used to calibrate hedges between different bonds. We can use the interest rate model to calculate duration and dollar duration measures that apply to all fixed income instruments, not just securities with fixed cash flows. Measuring and Hedging Interest Rate Risk Reading Veronesi, pp. 372-375

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Debt Instruments and Markets Professor Carpenter SR Duration and Hedging 2 Recall: dollar duration - Δ price/ Δ rates For securities like options that don’t have fixed cash flows, there may not be an explicit price-rate function to differentiate. But the binomial tree gives prices at the end of the first period (time h) in two different interest rate environments, which we can use to estimate dollar duration with respect to the short rate: Short Rate Dollar Duration Time 0.5 K u 0.5 r 1 u K d 0.5 r 1 d Asset price Short rate short rate \$dur = - K u - K d 0.5 r 1 u - 0.5 r 1 d Class Problems Time 0 Time 0.5 0.973047 0.947649 0.922242 0.5 r 1 u = 6.004% 0.970857 0.941787 0.5 r 1 d = 4.721% 0.976941 0.953790 \$1 par of 0.5- year zero: \$1 par of 1- year zero: \$1 par of 1.5- year zero: Recall the zero prices in our binomial tree below: Calculate the SR dollar duration for \$1 par of each of these zeroes:
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