How does price volatility affect the borrow APY?

The protocol does not guarantee liquidity; instead, it relies on the interest rate model to encourage it. In periods of extreme demand for an asset, the liquidity of the protocol (the tokens available to withdraw or borrow) will decline; when this occurs, interest rates rise, encouraging supply, and discouraging borrows. So in theory when there are rapid changes in prices, APY's should respond because both are driven by demand (or the lack thereof).