The Price Yield Reports are based on the inverse relationships between Price and Yield, which allows the user to calculate one from the other. The user can run various types of Price Yield Reports. See details on the following pages:
Note on the Calculations:
Price and yield have an inverse relationship. This means that given a yield, the Report can calculate the price.
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The following Reports detailed in this section will utilize this inverse relationship between any input and output offered in each Report.
See below the detailed explanation of the calculation for more details on the conceptual level, yet keep in mind that the reports use Taylor Expansion to achieve the highest level of accuracy possible.
This explanation regards price yield, yet the concept holds for other inputs and outputs.
First, stating the relationship between price and yield:
Where k represents the yield.
Next, to estimate the bond duration, take the first derivative of equation (1) with respect to theta.
To get an estimation of the convexity, take the second derivative of equation (1) with respect to theta.
Read more in Bond Scenario to understand duration and convexity.
To achieve higher accuracy, keep taking derivatives. Taylor Expansion sums an infinite amount of the functions' derivatives at a single point, thus it is much more accurate.