Free module · Options & volatility
Volatility: Measurement, Surfaces & Variance Risk
Separate what happened, what is forecast and what an option price implies.
realized variance · EWMA · HAR · implied volatility · term structure · convexity
The building blocks
Volatility measures the size of return variation. Historical estimates, future forecasts and option-implied values are different objects.
- Choose returns, sampling and horizon.
- Measure and forecast with transparent benchmarks.
- Translate option prices into implied quantities and stress the resulting exposure.
Lessons in this module
- Realized variance starts with squared returns
- EWMA as a causal variance baseline
- A multi-horizon realized-variance forecast
- Implied volatility is a model inversion
- Term structure through total and forward variance
- Strike convexity and a butterfly consistency check
- Vega requires a volatility-unit convention
- Variance exposure and the difference from arbitrage
Practice and apply
- Square intraday returns — Completed intraday log returns .01 and −.02 for a complete day.
- Extract interval variance — Annualized vol .2 at .5 years; .25 at 1 year; compatible moneyness conventions.
- Check local strike convexity — Same-expiry European call prices at strikes 90/100/110 are 13/8/4.
Work through the practice exercises · Quant development tools