Exchange rate stability
Since the onset of the COVID recession the exchange rate between the euro and dollar has appreciated by around 7%. To put this in perspective, over the course of 2008 financial crisis, the dollar-euro rate gyrated between 1.58 and 1.07, the yen-dollar between 90 and 123. In this paper Ilzetzki and al. analyze the reasons of this surprising exchange rate stability as well as what this missing volatility portends for the future of the global exchange rate system, not just at the center but for emerging markets and the periphery.
We will argue that a central driving force has been a collapse in international short-term and long-term interest differentials combined with an assumption in markets that the effective lower bound on interest rates is here to stay for a very long time. Relative volatility in conventional monetary policy has apparently been removed from the table for an extended period. The collapse of interest differentials not only reflects the global nature of the pandemic, but also the stunning decline in long-term global inflation differentials.

Will the Secular Decline in Exchange Rate and Inflation Volatility Survive COVID-19
Authors: Ethan Ilzetzki, Carmen M. Reinhart, Kenneth S. Rogoff
From: London School of Economics, World Bank, Harvard University
Hedging and exchange rate movements
The Broad Dollar Index rise during the COVID recession was not uniform: the currencies of net investor countries, such as the Japanese yen and the euro, appreciated against the dollar in both forward and spot exchange rate markets. In addition investor countries drew more on their Federal Reserve dollar swap lines. On the contrary, net debtor countries saw their currencies depreciate as they did not use their swap lines. Liao and Zhang develop a model that shows that exchange rate hedging coupled with intermediary constraints can explain these observed movements in exchange rates and swap line usage.

The Hedging Channel of Exchange Rate Determination
Authors: Gordon Liao, Tony Zhang
From: Federal Reserve Board