Thiruspace.com : SampleTopics : Curve Analytics 11.1.2
How Volatility impacts IR Swaption Pricing and Risk - Page 1 of 2
(An InterActive Model with Emphasis on Curve-Shifts and their Impact on Pricing/Risk)
Users with Login can input their own Curves using FileUpload utility.
For this page and the following, let's use the following YieldCurve for our analysis.
In a normal steep-shaped positive curve, the order of curves is Forward > Zero > Par (FZP), and the converse is true
in a inverted yield-curve scenario. Forward Rates have greater momentum than par rates, and they exhibit greater volatility.
A small change in par rates leads to a higher proportionate change in forward rates.
Forward rates calculated from cash-market yield curve
do not include any compensation for risk, nor any liquidity premium adjustment. While calculating these Forward
rates, transaction costs are assumed to be zero (in line with the pure expectations theory of Term Structure).
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Yield curve fitting can be done using one of the four following methods:
1. Linear Interpolation
2. Logarithmic Interpolation - where we use natural logarithms for discount factors, instead of using yield-levels per se.
3. Polynomial Fitting - using given vertices as polynomial factors and solving equation for y-axis.
4. Cubine Spline method.
In the Next session, you can see how to use Cubic-Spline method to create a "smoothed" forward curve,
whereby you can avoid the kinks associated with linear interpolation.
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