Large differences in implied (quoted for option prices) and historic (realised, i.e., actual movements in spot price) volatilities can be interpreted as relative over or under-pricing of options by the market.
These charts show one month historic volatility versus the one month at-the-money volatility quoted by the market for option prices. Risk Reversal vs. Spot: Risk reversals show the relative price difference between puts (downside expectation) and calls (upside expectation).
This chart illustrates the historic relationship between one month 25-delta risk reversals versus the underlying spot rate. Positive values indicate calls valued higher than puts, negative values indicate puts valued higher than calls.