Understanding Implied Volatility and Expected Moves (1σ, 2σ, 3σ)

 With Real Examples for Silver (IV = 80%) and Gold (IV = 30%)

Implied Volatility (IV) is one of the most important concepts in derivatives and risk management. It tells us how much the market expects an asset to move over the coming period, based on option prices. But how do we translate a quoted IV into an expected price move over various timeframes like a day, three days, a week, or a month?

In this post, we’ll explain:

• What implied volatility means

• How to calculate expected 1σ, 2σ, and 3σ moves

• Practical examples using Silver and Gold with assumed IVs and prices

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🧠 What Is Implied Volatility?

Implied volatility is the volatility “priced into” an option. It is the market’s consensus estimate of how much the underlying asset’s price is expected to move over a year — expressed in percentage terms.

But IV by itself isn’t directly a daily move. To estimate expected price ranges over shorter periods, we use the square-root-of-time rule:

$$\text{σ (over N days)} = \text{Annual IV} \times \sqrt{\frac{N}{252}}$$

Why 252? Because the financial markets typically use ~252 trading days per year to annualize volatility.

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📏 What Are 1σ, 2σ, 3σ Moves?

In a normal distribution:

• 1σ move (one standard deviation) means there’s ~68% probability the price stays within that range.

• 2σ move covers ~95% probability.

• 3σ move covers ~99.7% probability.

So if you can estimate σ over a timeframe, you can gauge how far the price might move — statistically — with decreasing probability as you go from 1σ to 3σ.

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📊 Assumptions

Metal	Current Price	Implied Volatility (IV)
Silver	₹250,000	80%
Gold	₹150,000	30%

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📌 Expected Moves Table

We compute expected volatility over:

• 1 day

• 3 days

• 1 week (5 trading days)

• 1 month (21 trading days)

Then scale for:

• 1σ = σ

• 2σ = 2×σ

• 3σ = 3×σ

📍 Formula

\text{Expected % Move} = \text{IV} \times \sqrt{\frac{T}{252}}

Where T = number of trading days.

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📉 Silver (IV = 80%)

Timeframe	√(T/252)	1σ Move	2σ Move	3σ Move
1 day	0.0564	±4.5%	±9.0%	±13.5%
3 days	0.0975	±7.8%	±15.6%	±23.4%
1 week	0.1581	±12.6%	±25.2%	±37.8%
1 month	0.2887	±23.1%	±46.2%	±69.3%

In price terms:

Timeframe	1σ (₹)	2σ (₹)	3σ (₹)
1 day	±11,250	±22,500	±33,750
3 days	±19,500	±39,000	±58,500
1 week	±31,500	±63,000	±94,500
1 month	±57,750	±115,500	±173,250

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📉 Gold (IV = 30%)

Timeframe	√(T/252)	1σ Move	2σ Move	3σ Move
1 day	0.0564	±1.7%	±3.4%	±5.1%
3 days	0.0975	±2.9%	±5.8%	±8.7%
1 week	0.1581	±4.7%	±9.4%	±14.1%
1 month	0.2887	±8.7%	±17.4%	±26.1%

In price terms:

Timeframe	1σ (₹)	2σ (₹)	3σ (₹)
1 day	±2,550	±5,100	±7,650
3 days	±4,350	±8,700	±13,050
1 week	±7,050	±14,100	±21,150
1 month	±13,050	±26,100	±39,150

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📌 Key Takeaways

🔹 Implied Volatility Is About Expectations

IV doesn’t tell you what will happen — it tells you what the market prices in as likely ranges.

🔹 Higher IV = Wider Expected Moves

Silver at 80% IV implies much larger short-term percentage swings than Gold at 30%.

🔹 Moves Grow With Time, But at √Time

For example, a 1-week move isn’t 5× a 1-day move; it’s roughly:

$$\text{√5} ≈ 2.24$$

times the 1-day move.

🔹 3σ Moves Are Rare but Possible

A 3σ move over 1 week for Silver at 80% IV is ±37.8% — huge, but within the bounds of statistical expectation.

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🧠 How Traders Use This

• Risk limits: Knowing your 1σ or 2σ range helps set position size.

• Option pricing: Expectation of daily moves feeds into fair value.

• Event planning: Big macro events can cause realized moves far beyond historical norms.

For example:

• If Silver’s one-day 1σ move is ~±4.5%, a move of ±9% would be a 2σ day, seen only ~5% of the time.

• A ±13.5% day (3σ) would be very rare — typically only ~0.3% of days.

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📌 Final Thought

Implied volatility isn’t just a number on a screen — it’s a probability distribution selector. Converting it into expected moves over different horizons demystifies what traders and markets are really pricing in.

If you’d like, I can turn this into a visual chart (PDF or PNG) showing expected ranges for silver and gold across time — useful for presentations, risk reports, or your own trading playbook.