"... that the liquidity trap became a possibility"
Whether we are in a liquidity trap or not, after the initial inflation fears in early 2009, right after the concerted central banks moves in late 2008 to contain the Lehman crisis, the inflation expectation has remained largely benign. And the demand for hedging inflation tail risk in outright cms caps, popular in 2009, has waned steadily. And, as of now, the convexity trades close to recent historical low, esp for shorter maturities.
As a result, CMS (constant maturity swaps) caps has cheapened relative to payers, as well, in terms of the price of a portfolio of a short ATMF payer vs long CMS single look cap with the same strike, with ATMF cash DV01 times the notional.
This cheapening has resulted in recent historical LOW break-evens for such a portfolio. Here the break-even means the amount (bps) the underlying rates should sell off to make a short payer/long CMS cap portfolio to break-even.
And USD rates show a similar trend, emphasizing the global downward repricing since the onset of the Great Recession.
Which is probably correct in pricing the inflation tail risks - given the elusive economic recovery and the super credibility of the central banks on both sides of the Atlantic.
We have witnessed a repricing of real rate since the crisis in both the economies
However, for euro, this situation can be interesting for someone positioning for other possible tail risk events in the monetary union. Given the current scenario, rates perhaps is not the best asset class for positioning for such a situation, but within rates universe, this long convexity package can be attractive. A typical tail events in rates are historically associated with a rally in rates and vol, but given the current levels of rates, it would not be surprising if we have a massive selloff instead, especially in the short end - (along with a steep flattening). Front-loading of risk premium is a case in point, another is the comparattively higher foreign investors share in german bonds compared to local investors, and an extreme third may be even a policy rate hike to prop up euro
