one of the research paper i am currently reviewing, its said that 3m ATMF implied volatility remains elevated, but risk reversal skew (3m, 25-delta) is minimal here is my question; why do we use 3m, 25-delta as a proxy to measure the level of implied volatility? what not at-the-money implied volatility?

Huh? The question doesn't make sense... The paper suggests that the 25-delta RR is used as a measure of skew (or vol of vol, although I am not sure this is used in the world of equities), rather than the level of vol per se.

It uses the 3m ATM to measure the level of implied volatility. it uses the 25-delta risk reversal to measure the skew steepness. In other words, you are comparing the implied volatility of a 25-delta call to the implied volatility of a 25-delta put.

The ATM vol and the price of the 25-delta RR (i.e. the measure of skew) can help you generate the mkt-implied risk-neutral distribution of the value of the underlying. Think of it as helping you generate a fan chart... It's not entirely clear what this has to do with the charts you show. Do you trade TWD NDFs?

execuse me for i am just a newbie in option trading, but why do we need to know the skew steepness? to know whether put is more expensive than call or something else? how could we do based on that information provide?

Firstly, it can provide you information about the risk-neutral probability distribution implied by the mkt. Secondly, if you disagree with how skew is priced (e.g. you think puts are too expensive), you can put on a position to express this view (1x2s, ladders etc).

thanks for your reply. my last question is how to we draw the skew stepness from the price of call and put?