Yield Duration and Convexity Relationships
We can derive the relationship between changes in the yield to maturity and the change in the market value of a standard fixed-income bond using a bit of algebra and calculus. Equation 6.1 is a general bond pricing equation very similar to equation 3.9 in Chapter 3.
The periodic coupon payments (PMT) and the principal (FV) to be redeemed in full at maturity are discounted at the yield per period (y). The settlement date is t days into the T-day period and there are N periods to maturity counting from the beginning of the current period. Here the present value of the future cash flows is the market value ...
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