Implied vs Realized Volatility
Implied is what you pay. Realized is what you get. The gap between them is where every options trader lives.
Two different things
Realized volatility (RV) is what the underlying actually did. It is computed from price history. You take a window of past returns, compute their standard deviation, and annualize. It is a backward-looking measurement of how much the stock moved.
Implied volatility (IV) is what the options market expects the underlying to do. It is extracted from option prices. You take the market price of an option, run it through Black-Scholes in reverse, and solve for the volatility input that would make the model output match the market price.
Both are quoted in annualized percentage terms. They look identical on a chart. They are not the same thing.
How the two relate
Over time, IV and RV track each other loosely. They share the same underlying reality. When the market becomes more volatile, both numbers tend to rise. When it calms down, both tend to fall.
Two patterns are visible in the chart. First, IV and RV move together. Major moves in one usually show up in the other. Second, IV usually sits above RV. This is not random. It reflects a structural premium that options buyers pay for protection. The gap is the subject of the next lesson.
How realized volatility is computed
The standard formula is the annualized standard deviation of log returns over a rolling window. For a 30-day RV calculation:
- Compute daily log returns:
r_t = ln(P_t / P_{t-1}) - Compute the standard deviation over the last 30 daily returns
- Annualize by multiplying by the square root of 252 (trading days per year)
Different windows give different RV numbers. A 5-day RV captures very recent behavior. A 60-day RV captures the medium-term backdrop. Both are correct; they just answer different questions.
How implied volatility is computed
There is no closed-form solution. You take the option's market price, plug it into a pricing model along with strike, time to expiry, spot, and the risk-free rate, and solve numerically for the volatility input that reproduces the market price. The result is the IV for that specific option.
Different strikes have different IVs. Different expiries have different IVs. The full set of IVs across strikes and expiries is called the volatility surface. Lessons L.12 and L.13 cover its shape.
Why the relationship matters
If you buy an option, you have paid for IV. You make money if RV ends up higher than what you paid for, plus enough to cover decay. If you sell an option, you have received IV. You make money if RV comes in lower than what you sold.
This is why long options is sometimes called "long volatility" and short options is sometimes called "short volatility." The position is, mechanically, a bet on the spread between IV (what you paid or received) and RV (what actually plays out).
Realized vs implied at the index vs single-name level
Index IV (VIX) is usually higher than single-name average IV. This sounds backward (a basket should be less volatile than its components) and it is. The reason is correlation risk: the VIX prices in the chance that all the components fall together. In normal markets, components diversify each other and the index moves less than its parts. In a crash, correlation spikes to 1 and the index moves with the worst components.
Index options are pricing the crash scenario. Single-name options are not. This matters when comparing IVs across different underlyings.
Where this lesson points
The next lesson, on the variance risk premium, builds directly on the IV-RV gap. The two lessons after that (skew and term structure) explore how IV varies across the options surface. The Greek that connects all of this to your P&L is vega, which you saw in L.08.
Once you internalize that options are priced in IV and your P&L depends on RV, the rest of the curriculum starts to assemble itself. Every strategy is, at root, a position on the IV-RV relationship at some specific part of the surface.
What you carry forward
- Realized volatility is what actually happened. Implied volatility is what the market expects.
- IV is extracted from option prices. RV is computed from price history.
- IV usually sits above RV by a structural margin (the variance risk premium).
- Long options profits when RV exceeds IV. Short options profits when IV exceeds RV.
- Always check IV vs recent RV before opening a position.