Course Map: Inference & the Volatility Tools

Welcome to Tier 200, and to the engine room of the institute.

In Tier 100 you learned two complementary skills. SVI 101 taught you to read market data honestly — to ask whether a number is evidence. SVI 102 taught you the probability that generates that data — the models behind the platform's outputs. Statistical inference is the bridge between them. It is the formal craft of reasoning backward: from a finite sample of data to a statement about the unknown truth that produced it — with the uncertainty made explicit and honest. This is where you stop merely having ideas about the market and start testing them.

Every inference problem is one of three tasks, and this course teaches all three. Point estimation — give the single best value for an unknown (and how it's built). Confidence sets — wrap that value in an honest interval. Hypothesis testing — decide whether an effect is real or chance. You met each informally in 101; here they become rigorous, and each is anchored to a real SVQ volatility tool so the math never floats free.

Here is the road through the five modules:

1. Estimation: Sampling Distributions & Maximum Likelihood — how estimators are actually built, culminating in maximum likelihood, the engine under nearly every fitted model in finance. Anchored to SVQ's IV Rank, IV Percentile, and Z-score — three estimates of where implied volatility sits today.
2. Confidence Intervals & the Bootstrap — putting honest error bars on any estimate, including by resampling when no formula exists. Anchored to realized-volatility windows (5/20/60-day) and how much each one can be trusted.
3. Hypothesis Testing: Significance, Errors & Power — the formal machinery of significance, Type I/II errors, power, and the p-value (and what it is not). Framed as the question "is implied volatility genuinely richer than realized?"
4. Comparing Volatilities: Implied vs Realized — the applied test in full, producing the volatility risk premium, VRP = σ_IV² − σ_RV², one of the most-watched edges in options.
5. Non-Parametric Tests & Percentiles — rank-based methods that make no distributional assumption, anchored to HVP and HVR, the historical-volatility percentile and rank you already met.

The course closes with a graded assessment that runs the whole inference toolkit. Pass it and 201 counts toward your Tier 200 credential; earn honors and you are flagged for the honors track.

When you finish, you will be able to take any SVQ reading and not just interpret it but interrogate it: estimate the quantity, bound its uncertainty, and test whether what you are seeing could be chance. SVI 202 then extends inference to relationships between variables — regression and time series, including the GARCH volatility models that the EWMA of 102 only previewed.

Let's begin where inference begins — with how an estimate is actually made.