# Volatility Analysis and Risk Forecasts Distinguish realized volatility, implied volatility and forecast uncertainty. Use this workbook alongside the course. Write your answers before opening the solutions. Practical work is self-reviewed; scored knowledge checks are in the Academy. ## 1. Realized measures ### Return sampling Realized volatility summarizes observed return variation over a defined interval. Specify return type, sampling frequency and window. Changing any of these changes the measured quantity, so two values called volatility may not be directly comparable. ### Close-to-close estimates Close-to-close estimates use sampled returns and can miss intraperiod paths. A day with a large excursion and little closing change may contribute little to that measure despite substantial intraday risk. ### Range-based estimates Range-based measures use high-low or other bar information under particular assumptions. They can capture information absent from close-only returns, but gaps, market microstructure and incomplete coverage can affect their interpretation. ### Annualization assumptions Annualization converts a sampling-scale estimate under assumptions about time aggregation. Square-root-of-time scaling is not a universal law when returns are dependent or volatility changes. Label both the original frequency and conversion assumptions. ### Worked example Two days each close unchanged. One barely moves; the other rises sharply and reverses. Close-to-close returns are zero for both, but their intraday exposure paths differ substantially. ### Independent exercise Specify two measurements that would distinguish those days and explain why a closing-return measure alone is incomplete for intraday risk. My inputs and assumptions: My calculation or decision: Evidence that would change my conclusion: ## 2. Dynamics ### Clustering Volatility clustering describes periods in which large or small movements tend to occur near similar movements. It does not mean the direction of the next return is known. A magnitude pattern is different from a directional signal. ### Jumps Jumps are abrupt changes that a smooth variation model may handle poorly. Their identification depends on sampling and a specified method. Include event and data-quality investigation before assigning every large observation to a market jump. ### Intraday seasonality Intraday seasonality can affect typical activity and spread. Compare like times and sessions when estimating a baseline. A time-of-day pattern can change and should be evaluated across dates rather than assumed permanent. ### Longer-horizon aggregation Longer-horizon risk aggregates more than a simple count of short intervals when dependence, changing volatility or gaps matter. Stress scenarios complement a point forecast but do not establish a complete worst-case bound. ### Worked example A model trained on quiet hours systematically underestimates movement around scheduled releases. The problem may be a mismatched conditional baseline, not merely a need to multiply every forecast by the same constant. ### Independent exercise Design a diagnostic separating ordinary-session errors from event-window errors while avoiding definitions chosen only after the worst outcomes. My inputs and assumptions: My calculation or decision: Evidence that would change my conclusion: ## 3. Implied measures ### Option prices and implied volatility Implied volatility is inferred from an option price through a chosen valuation model and inputs. It is not a directly observed future realized volatility. Different pricing assumptions or data quality can affect the inferred value. ### Maturity dependence Maturity matters: an option expiring tomorrow and one expiring months later reflect different horizons. Compare like maturities or use an explicit interpolation method, recording its assumptions. ### Skew Skew describes variation across strikes or related moneyness measures. A single at-the-money value does not summarize all nonlinear exposure. Inspect which portion of the surface is relevant to the position. ### Risk premium interpretation limits The difference between implied and later realized volatility is not automatically an accessible risk-free profit. Trading volatility involves option pricing, hedging, costs, jumps and risk premia; a simple subtraction omits those mechanics. ### Worked example Two options have different implied volatilities but different maturities and strikes. Calling one cheap solely because its number is lower ignores that they reference different portions of the surface. ### Independent exercise List the fields needed for a meaningful implied-volatility comparison and one reason the comparison still would not be a complete trading decision. My inputs and assumptions: My calculation or decision: Evidence that would change my conclusion: ## 4. Forecast evaluation ### Rolling estimates A rolling forecast must use only data available before its target period. Save the forecast when made, then compare it with the later realized measure. Recomputing old forecasts with revised inputs can create an unrealistically clean history. ### Point-in-time inputs Point-in-time inputs include publication and correction timing. A series stored today may contain values unavailable at the historical decision. Preserve data versions where revisions can affect evaluation. ### Error metrics Choose error metrics suited to the target and decision. Squared error emphasizes large errors; absolute error weights them differently. Do not select the metric only because it favors the preferred model. ### Stress overrides as governance decisions Stress overrides are governance choices that alter behavior when conditions fall outside ordinary assumptions. Define triggers, ownership and review rather than presenting an ad hoc override as part of an unchanged forecast model. ### Worked example Forecast A has one very large miss and many small misses; B has moderate misses throughout. Their ranking can depend on the error metric, so the relevant loss function should be specified before comparison. ### Independent exercise Write an evaluation protocol naming the target, forecast timestamp, error metric and handling of revised observations. My inputs and assumptions: My calculation or decision: Evidence that would change my conclusion: ## Course project Compare several volatility estimates and document where their forecasts fail. ### Self-review rubric - Concepts and reasoning: 25% - Calculations, data and evidence: 30% - Process and risk controls: 25% - Limitations and communication: 20% Record one correction and one next practice task. This rubric is not automatically graded. ## Worked solutions ### Exercise 1 High-low range and intraday sampled variation are possible choices. Record their data coverage and frequency. They describe different aspects of the path and should not be treated as interchangeable forecasts. ### Exercise 2 Predefine event windows from the calendar, compare forecast errors in each group and report sample sizes. Keep a later evaluation period for any revised model and preserve the original errors. ### Exercise 3 Match underlying, timestamp, maturity, strike or moneyness, model and price quality. Then consider spread, hedging assumptions and exposure. A normalized comparison is evidence, not an automatic executable opportunity. ### Exercise 4 Use a fixed target definition and stored forecasts, select the metric for the decision objective, retain original data vintages and report revisions separately. This distinguishes prospective performance from retrospective reconstruction. ## Further reading - https://www.itl.nist.gov/div898/handbook/ - https://www.cmegroup.com/education