Question ID: 403
Regulation Reference: Risk-Free Interest Rate - General questions
Article: 43
Status: Final
Date of submission: 23 Jul 2015
Question
For the SCR interest rate risk scenario shift (or Matching Adjustment shift/Volatility Adjustment shift), once the shift applied, should the modified zero coupon curve be recalculated by applying the Smith-Wilson method? My understanding is yes, as we need to take the shift into account when do interpolation, like to retrieve discount factor of 1.3 years. Is it correct?
About Smith-Wilson method itself: For a currency, EUR for example, given the swap instruments, by applying the Smith-Wilson calculation process (we call strip process), a zero coupon rate curve will be generated as a result. If we take this zero coupon rate curve as input, and apply the Smith-Wilson strip process again, a new zero coupon rate curve will be generated. The first zero rate curve will be different from the second one, because the coefficient of the Smith-Wilson base function will be different after two strips. Which mean, if asking for the discount factor for 1.3 years (when interpolation happens), the two zero rate curves will give different value. The question is: how many times of strip should apply? Always once, or twice?
EIOPA answer
These appear to be two questions: one on the SCR-shock and the other on valuation.
The SCR-shock, upwards and downwards, follow from applying a piecewise linear calculation instruction to be applied to the Smith-Wilson spot yield curve.
As a result this shocked yield curve itself is not of the Smith-Wilson type anymore.
As regards Smith-Wilson, indeed applying it to swap instruments results in Smith-Wilson zero-coupon type output.
In case these swap instruments imply a square cash-flow matrix, this input can be inverted right-away into a diagonal (zero-coupon) cash-flow matrix.
As a result there will be no difference in the parameters of the Smith-Wilson present value function, even not for the convergence parameter alpha.
So, results will not only coincide for integer maturities but also for fractional ones.