Risk Premium

Risk premium is the extra return an investor expects for taking on a risk, above what they'd get from a virtually risk-free option like a short-term government bond. It's compensation for uncertainty: if you're going to tie up money in something that could lose value, you want the potential payoff to be higher than the "safe" alternative, otherwise there's no reason to take the risk.

In practice it shows up in several places. The equity risk premium is the extra return stocks are expected to deliver over risk-free government debt, reflecting the risk of owning a piece of a business versus lending to a government that's assumed not to default. In options pricing, the same idea appears as extrinsic value, the portion of an option's price that isn't just its intrinsic, "already in the money" value, but rather what buyers are willing to pay for the time and volatility risk the seller is taking on. In credit markets, it's the extra yield a risky borrower has to offer over a safer one.

The nuance that trips people up: risk premium is a forward-looking, expected concept, not a guaranteed one. It describes what investors demand on average for bearing risk, not what any single trade will actually return. A stock or option can easily underperform the "risk-free" benchmark over any given period even though it carried a positive risk premium going in. It's also not the same thing as volatility itself; volatility is a measure of how much prices move, while risk premium is the price investors put on being exposed to that movement.

Calling risk premium a simple synonym for extrinsic value (as older glossaries sometimes do) collapses a broad concept into one narrow application. Extrinsic value in options is one specific expression of risk premium, not the whole idea.