This is the capstone — one graded run across the entire course. The questions roam over everything: how realized volatility is the annualized standard deviation of log returns while implied volatility is the number you back out of an option’s price, and why the gap between them is the whole game; how variance swaps pay on vol squared and pack a convexity that vol swaps don’t; how the VIX is the square root of a 30-day variance-swap rate built from a strip of SPX options, why its curve usually sits in contango, and what that did to short-vol funds in February 2018; why implied tends to print above realized and who collects that premium; how a long straddle bets on a big move in either direction; how dispersion is a short bet on correlation dressed up as a vol trade; and how a tail hedge is a convex payoff you have to keep paying for. There is no formula sheet and no second guess — read all the options before you commit, because each wrong one is a trap that has caught a real trainee.
How this exam works
This is a graded exam. Questions arrive one at a time. Once you submit an answer it is final — there is no going back, no retries, and a wrong answer simply fails that question. Your score stays hidden until the very end, where you need 70% to pass. Slow down and read every option before you commit.
Realized volatility over a sample of daily returns is computed how, and why the square root of 252?
Select an answer to continue.
Course Recap
Whatever your score reads, the framework you just stress-tested — realized vol as the annualized dispersion of returns and implied vol as the price baked into options, the variance and vol swaps that turn that gap into a clean payoff, the VIX as the square root of a 30-day variance-swap rate with a curve that usually bleeds the long-VIX roller, the volatility risk premium that pays sellers for bearing tail risk, the straddles and strangles that bet on movement, the dispersion trade that is really a short-correlation position, and the convex tail hedge you have to finance and monetize — is the working map of how volatility itself is traded as an asset. Here is the whole course in one glance.
Big picture
Volatility Trading, in one glance
- Volatility Trading
- Realized vs implied vol
- Realized = stdev of log returns, annualized by root-252
- Implied = vol backed out of an option price via vega
- Both annualized, so directly comparable
- Smile/skew + term structure = the vol surface
- The implied-minus-realized gap is the trade
- Variance & vol swaps
- Vol swap pays linearly in realized vol
- Variance swap pays in realized variance (vol squared)
- Vega notional = variance notional times 2 times strike vol
- Long variance = long convexity, so strike above ATM IV
- Replicated by a 1/K-squared option strip (the VIX link)
- VIX & term structure
- VIX = root of a 30-day model-free SPX variance rate
- Not tradable directly — only futures, options, ETPs
- Rule of thumb: VIX 16 means about a 1% daily move
- Curve usually in contango, so long VIX bleeds (VXX decays)
- Backwardation in panics; XIV blew up Feb 2018
- Volatility risk premium
- VRP = implied minus realized, positive on average
- Exists because investors buy protection, sellers want pay
- Harvested by selling options/variance, short VIX futures
- Negatively skewed: pennies in front of a steamroller
- Fair pay for tail risk, not free alpha
- Straddles & strangles
- Long straddle = call + put at the same strike
- Break-evens = strike plus or minus total premium
- Strangle = OTM split strikes, cheaper, needs a bigger move
- Long vega, long gamma, short theta
- Vol crush drains a straddle after earnings
- Dispersion trading
- Index IV below weighted-avg single-name IV (correlation < 1)
- Implied correlation = index variance over avg variance
- Sell index vol + buy single-name vol = short correlation
- Profits if realized correlation < implied
- Blows up when correlations spike to 1 in a crash
- Tail hedging
- Convex payoff from deep OTM puts / long vol
- Small bleed in calm, explodes in a crash
- You finance the bleed by paying the VRP
- Put spreads, laddering, monetizing the spike
- Small allocation + barbell with a short-vol income book
- Realized vs implied vol
Key Takeaways
What you now own
You can treat volatility as an asset in its own right: measure realized vol as the annualized standard deviation of log returns, read implied vol straight out of an option’s price, and see that the gap between them — implied minus realized — is the game the whole market is playing. You can turn that gap into a clean payoff with vol swaps and variance swaps, explain why variance is convex and trades above ATM IV, and recognize the 1/K-squared option strip that both replicates variance and builds the VIX. You know the VIX is the square root of a 30-day variance-swap rate, that you trade it only through futures, options, and ETPs, that its contango quietly bleeds long-VIX products, and what that bleed did to XIV in February 2018. You can define the volatility risk premium, explain why selling it is collecting pennies in front of a steamroller, and price a long straddle’s break-evens while naming its long-vega, long-gamma, short-theta profile and the vol crush that ambushes it after earnings. You can read dispersion as a short-correlation trade, compute implied correlation from index and single-name variance, and see why it detonates when correlations rush to one. And — the payoff of the whole course — you can build a convex tail hedge, finance its bleed, monetize its spikes, and judge it by the only thing that matters: how the whole portfolio compounds and draws down through a crisis. That is the volatility-trading toolkit, end to end.