Variance risk premiums mark the difference between implied (future) and past volatility. They indicate changes in risk aversion or uncertainty. As these changes may differ or have different implications across countries, they may cause FX overshooting and payback. The effect complements the simpler argument that rising currency volatility predicts lower FX carry returns. Academic papers support both effects empirically.

Aloosh, Arash (2014), “Global Variance Risk Premium and Forex Return Predictability”, MPRA Paper No. 59931, November 2014

Bakshi, Gurdip, and George Panayotov (2013), “Predictability of Currency Carry Trades and Asset Pricing Implications”, Journal of Financial Economics 110 (2013), pp. 139–163

The below are excerpts from the papers. Emphasis and cursive text have been added. 

Why variance risk premiums are valuable predictors

“Variance risk premiums (VRPs) [are defined as] the difference between option-implied and realized stock market variance…
A parsimonious intuition for the predictive power of stock market volatility indices is as follows: a volatility index [based on options-implied volatility] measures the expectation of stock market volatility over the next period. When a…volatility index is significantly higher than the [past] realized…volatility [denoting a positive variance risk premium]…investors expect higher uncertainty over the next period. As a result, domestic agents require higher returns on their domestic and foreign investments. Therefore, domestic stock prices…decrease to compensate domestic agents to invest in the domestic stock market, and nominal spot exchange-rates [values of foreign to domestic currencies]…decrease to compensate them to invest abroad. However, nominal exchange-rates should adjust somehow to compensate both domestic and foreign investors, thus when the expected uncertainty of domestic agents increases relative to that of foreign agents, the nominal spot exchange-rates decrease, which predict higher nominal spot exchange-rates in the future.”
[Aloosh 2014]

N.B. The author interprets local equity volatility as specific to the local agent or local economy, not just the local assets. Therefore it would affect the premiums charged on all assets that local agent invests in.

“Moreover, heterogeneity in exposure to the global VRP, specifically the high exposure of the low-interest-rate countries and the low exposure of the high-interest-rate countries, generates a currency risk premium. In a complete market…the domestic agent with a higher exposure to the global VRP is exposed to more uncertainty in periods where global uncertainty is high. As a result, the equilibrium domestic currency appreciates to compensate the domestic agent for investing in the foreign bonds (as the domestic agent requires higher returns). At the same time, the higher uncertainty pushes down the domestic interest rate. The lower spot exchange rate and the lower domestic interest rate predict a higher excess forex return.”
[Aloosh 2014]

Empirical evidence for VRP and other volatility effects

“I build end-of-month series from December 1999 to December 2011… The local variance risk premium…is measured as the difference between the end-of-month risk-neutral expected variance and the end-of-month realized variance… Local equity VRPs can be estimated as the difference between the squared volatility indices and the realized variance of the respective equity indices, and therefore they measure aggregate volatility uncertainties. The global VRP is constructed as the average of local equity VRPs in four major countries (the US, UK, Japan and Europe), and thus it captures investors’ common expectations of aggregate volatility uncertainty.
This paper…finds that local and global equity variance risk premiums (VRPs) predict forex returns of the [British] pound, the [Japanese] yen, and the euro against the U.S. dollar, with an adjusted R-square of up to 17%…For example, when the local equity VRP increases by one percent in the U.S. the expected pound-dollar forex return increases…by around 5%…and when the global equity VRP increases by one percent, the expected pound-dollar forex return increases by around 3%.”
[Aloosh 2014]

“Even if potentially lucrative, carry trades also present substantial downside risks… Our innovation is the focus on time series predictability, as opposed to the cross section of currency portfolio returns… We build time series of monthly carry trade payoffs, using spot and forward exchange rates of G-10 currencies and accounting for bid–ask spreads… Our sample starts in January 1985, ends in August 2011, and encompasses about 27 years of currency market history.
Monthly payoffs of dynamic carry trades can be predicted in-sample, using as predictors changes in a commodity price index, changes in average [historic] currency volatility, and a variable that captures global liquidity…
Moreover, we investigate the robustness of our results using other predictors, in particular, the term structure variables…as well as the change in VIX…The presence of these additional variables does not appear to diminish the predictive ability of our predictors.”
[Bakshi and Panayotov, 2013]

 “We explore a variable that could serve as a proxy for uncertainty in global currency markets and consider specifically the normalized log changes in average currency volatility…For each currency, we construct monthly volatility as the square root of the sum of squares of daily log changes in the exchange rate against the US dollar over a month, which is then averaged across the G-10 currencies in the sample.
In considering average currency volatility as a predictor, we are guided by the perception…that the profitability of carry trades appears to decline in volatile currency markets…
[Empirically] a high level of [changes in currency volatility] predicts lower next-month carry trade payoffs.”
[Bakshi and Panayotov, 2013]

 “Moreover, I run a ‘horse race’ among three currency predictors, the commodity and the currency volatility factors of Bakshi and Panayotov (2013) and the global VRP to predict currency carry trade returns, bilateral forex returns, and cross-country equity return differentials.
I find first that the global VRP has significantly higher predictive powerfor the carry trade returns, the bilateral forex returns, and the cross-country equity return differentials.
Secondly, I find that the global VRP, which is primarily an equity predictor, has similar predictive power for a bilateral forex returns and the respective cross-country equity return differential, and that the commodity and the currency volatility factors…also have similar predictive power for a bilateral forex return and the respective cross-country equity return differential.”
[Aloosh 2014]