# PRIIPs bootstrap for Category 3 MRM - bonds - future values to maturity

PRIIPs regulation Annex 2 states in Point 20 that bootstrapping is to be used to infer the expected distribution of prices or price levels for the PRIIP’s underlying contracts from the observed distribution of returns.

For a product based on a government bond this approach seems to be inefficient/wrong since there is some knowledge about the way the value of the bond will behave in the future. Namely, it should be expected that the bond will drop to its face (nominal) value. However, if I am correct in understanding what bootstrapping based on historical values will do, this will not be accounted for in the bootstrapping approach?

Especially if the historical data is collected where the value of the bond has been (in average) rising (e.g. mid or early term of a long term bond) or (in average) stable. In this case, bootstrapping will produce an average curve (among others) that is not falling down to the face value. Thus, for government bonds we would see something quite extraordinary at maturity :)

This is quite problematic since all of the quantiles will be overestimated leading to an overestimate in VaR!

Since there is no mention of "domain knowledge" in PRIIPs (Annexes), how would you approach this problem? If you do not find this to be a problem could you please explain why you think so?

## 1 Answer

In the case of a govt bond, shouldn't the simulation be based on a (govt bond) curve (point 23 in the annex) in which case as time passes in your simulation you will recompute the bond price from shorter and shorter tenor points on the curve, thus ensuring that the bond price converges to its nominal value at maturity ?

• Thanks for the reply :) Could you please elaborate on the answer a bit more since I do not understand it fully. From what I understand from Annex (and flow diagrams) we should have bootstrapping in the case of curves too. You would have multiple bootstrapping procedures? After you move to the next (tenor) point you would bootstrap again (from the values from that point from maturity to maturity)? How would you include a curve obtained from PCA into this? – iugrina Nov 23 '17 at 16:10
• Some of the questions are clear from the point 23.b, of course :). Still, would appreciate a bit more elaboration (or an example) if you have time ;) – iugrina Nov 23 '17 at 16:59
• Let's say the curve is a curve of govt bond par rates indexed by tenor. Using the procedure described in 23.a (reduction of the curve to 3 factors trough a PCA decomposition) you simulate the curve factors returns along your simulation time steps, then at each time step you compute the curve par rates returns from the PCA, then the curve par rates as in 23.b, then from the curve par rates you interpolate the par rate for the remaining maturity of your bond, and finally from these simulated par rates you recompute the bond prices at each time step. – Antoine Conze Nov 23 '17 at 17:17
• Thanks. I don't see at the moment the convergence to face value from this procedure but I will try it :) – iugrina Nov 23 '17 at 17:34
• The convergence will follow from the fact that you simulate rates and then plug these rates into a yield to price calculator to obtain prices. As remaining bond maturity goes to zero the yield to price calculation will converge to the bond face value. – Antoine Conze Nov 23 '17 at 17:40