Skewness risk plays an important role in hypothesis testing.
Benoît Mandelbrot, a French mathematician, extensively researched this issue.
In options markets, the difference in implied volatility at different strike prices represents the market's view of skew, and is called volatility skew.
(In pure Black–Scholes, implied volatility is constant with respect to strike and time to maturity.)
A bond will either pay the full amount on time (very likely to much less likely depending on quality), or less than that.