Since the beginning of this year, LIBOR rates have ceased in some markets like GBP, CHF, and JPY and rates pricing has moved into the RFR space, using compounded overnight rates as the underlying for cap-/floor(lets). My questions now are concerned with the building of a vol surface based on broker quotes of normal par vols (absolute strikes, yearly expiries, backward looking with quarterly compounding), and, in particular, caplet stripping:

1. what is the correct approach to bootstrap implied caplet vols if one wants to value caplets based on the Lyashenko/Mercurio expiry adjustment; basically, instead of using the accrual start date $T_S$ as the expiry of the option like we did for LIBORs, one uses an "extended" maturity $T_S+(T_E-T_S)/3$ to account for the fact that we are dealing with a backward looking rate that is still stochastic up until the last fixing occurs at $T_E$ but the volatility decays linearly within the accrual period). @Daneel Olivaw gave a splendid answer & derivation based on the above paper in this thread. My goal would be something simple for caplet vols (preferably piecewise linear or even constant) but I'm struggling how to achieve this with the "new" adjusted maturity.

2. how would the stripping change if we know that the quoted implied par vols are based on the fact that interdealer brokers assume a constant vol (instead of a linearly decaying one) within the accrual period. Then, no maturity adjustment is needed - we simply use $T_E$ as the caplet expiry date. It's clear that what matters for pricing is total variance of the compound rate, and we can achieve the same variance using a tuple of either $(\sigma_{implied}^{decaying}, T_S+(T_E-T_S)/3)$ or, alternatively, the broker quote $(\sigma_{implied}^{constant}, T_E)$. How does this factor into caplet stripping?

3. any idea on surface construction for a non-quoted tenor (e.g. options on 1m or 6m compound rates)? how could we up-/down-scale the surface to price such options?

Since the beginning of this year, LIBOR rates have ceased in some markets like GBP, CHF, and JPY and rates pricing has moved into the RFR space, using compounded overnight rates as the underlying for cap-/floor(lets). My questions now are concerned with the building of a vol surface based on broker quotes of normal par vols (absolute strikes, yearly expiries, backward looking with quarterly compounding), and, in particular, caplet stripping:

1. what is the correct approach to bootstrap implied caplet vols if one wants to value caplets based on the Lyashenko/Mercurio expiry adjustment; basically, instead of using the accrual start date $T_S$ as the expiry of the option like we did for LIBORs, one uses an "extended" maturity $T_S+(T_E-T_S)/3$ to account for the fact that we are dealing with a backward looking rate that is still stochastic up until the last fixing occurs at $T_E$ but the volatility decays linearly within the accrual period. @Daneel Olivaw gave a splendid answer & derivation based on the above paper in this thread. My goal would be something simple for caplet vols (preferably piecewise linear or even constant) but I'm struggling how to achieve this with the "new" adjusted maturity.

2. how would the stripping change if we know that the quoted implied par vols are based on the fact that interdealer brokers assume a constant vol (instead of a linearly decaying one) within the accrual period? Then, no maturity adjustment is needed - we simply use $T_E$ as the caplet expiry date. It's clear that what matters for pricing is total variance of the compound rate, and we can achieve the same variance using a tuple of either $(\sigma_{implied}^{decaying}, T_S+(T_E-T_S)/3)$ or, alternatively, the broker quote $(\sigma_{implied}^{constant}, T_E)$. How does this factor into caplet stripping?

3. any idea on surface construction for a non-quoted tenor (e.g. options on 1m or 6m compound rates)? how could we up-/down-scale the surface to price such options?