Volatility: Historical vs Implied, IV Rank, Smile & India VIX — Options Trading for Programmers

Options are really instruments for trading volatility, so this lesson earns its place. Get volatility right and the strategies in the next lessons make complete sense; get it wrong and you will keep buying high and selling low.

Two kinds of volatility

Historical (realised) volatility (HV) — how much the underlying actually moved in the past, computed from its returns. It is a fact about history.
Implied volatility (IV) — how much the market expects it to move in the future, backed out of option prices (Lesson 5). It is a forecast.

The gap between them is itself a signal. When IV is much higher than recent HV, options are “expensive” relative to how the market has actually been moving — good conditions to sell premium. When IV is below HV, options look cheap.

import numpy as np

def historical_vol(closes, periods=252):
    rets = np.diff(np.log(closes))          # daily log returns
    return rets.std() * np.sqrt(periods)    # annualised

# e.g. 30 days of Nifty closes -> realised vol, compare with IV from the chain

The number that matters: IV rank / IV percentile

Here is the trap: “IV is 12%” tells you almost nothing on its own. Is 12% high or low? It depends entirely on this underlying’s normal range. Nifty at 12% IV might be calm; a volatile stock at 12% might be unusually quiet. So we normalise:

IV Rank — where current IV sits between its 1-year low and high: (IV_now − IV_low) / (IV_high − IV_low). An IV rank of 80% means IV is near the top of its yearly range.
IV Percentile — the % of days in the past year that IV was below today’s level.

The rule of thumb almost every premium-seller uses: sell options when IV rank is high (premium is rich, likely to fall) and buy / go long volatility when IV rank is low (cheap, likely to rise). This works because of the most important property of volatility, below.

Volatility is mean-reverting

Unlike price, volatility tends to revert to a mean. Big spikes (panic) calm down; long calm periods eventually get a shock. This is the engine under most income strategies: sell expensive options when everyone is fearful (high IV), and let IV fall back to normal (IV crush in your favour). It is also why selling volatility feels like “free money” for long stretches — right up until the rare spike that pays out all the claims at once. Respect that tail (Lesson 10).

The volatility smile and skew

Black-Scholes assumes one constant volatility for all strikes. Reality disagrees. If you compute IV for every strike, you do not get a flat line — you get a smile or, for indices, a skew: out-of-the-money puts usually trade at a higher IV than calls. Why? Because investors pay up for downside crash insurance (puts), and markets fall faster than they rise. This skew is information: it tells you how the market is pricing fear. It also means a single BS “IV” is a simplification — each strike has its own.

India VIX: the fear gauge

India VIX is the market’s expected volatility of the Nifty over the next 30 days, derived from Nifty option prices (NSE publishes it live). It is the Indian cousin of the US VIX, and it behaves like a fear gauge:

Low VIX (say ~10–13) — calm, complacent markets. Option premiums thin.
High VIX (spikes to 20, 30, 40+) — fear, big expected moves, fat premiums. These spikes almost always come when the market is falling (VIX and Nifty are strongly negatively correlated).

For an options trader, India VIX is a quick daily read on the whole environment: are premiums rich or thin right now, and is fear rising or falling? Pull it alongside your option chain and let it shape whether you are in a buying or selling mood.

Pitfalls

Trading the raw IV number. Always ask “high or low for this underlying” — use IV rank/percentile, not the bare figure.
Shorting volatility right before a known event. IV is high before results/budgets for a reason — a big move may be coming. IV crush helps sellers only if the move doesn’t.
Assuming one IV for the chain. The smile/skew is real; OTM puts are usually dearer. Price each strike on its own IV.

Recap

Historical vol is what happened; implied vol is what’s expected. Judge IV by its rank/percentile, not the raw number — sell high, buy low — because volatility is mean-reverting. The smile/skew shows BS’s flat-vol assumption is only an approximation (OTM puts cost more). India VIX is the 30-day fear gauge; watch it daily.

Next: Lesson 7 — Directional Strategies, where we put this to work with covered calls, protective puts and cash-secured puts.