Analyze historical swings, log returns, and annual volatility fast. Test multiple periods and trading days. Understand equity compensation risk before making career decisions today.
| Observation | Closing Price | Notes |
|---|---|---|
| 1 | 100.00 | Starting reference price. |
| 2 | 102.00 | Early upward move. |
| 3 | 101.00 | Small pullback. |
| 4 | 105.00 | Momentum improves. |
| 5 | 107.00 | Trend continues higher. |
| 6 | 106.00 | Minor decline. |
| 7 | 110.00 | Volatility expands. |
| 8 | 108.00 | Short-term reversal. |
| 9 | 111.00 | Recovery appears. |
| 10 | 115.00 | New local high. |
1. Log Return: r = ln(Pt / Pt-1)
2. Simple Return: r = (Pt - Pt-1) / Pt-1
3. Sample Standard Deviation: s = sqrt( Σ(r - r̄)² / (n - 1) )
4. Annualized Volatility: σannual = s × sqrt(periods per year)
5. Black-Scholes d1: d1 = [ln(S/K) + (r - q + 0.5σ²)T] / (σ√T)
6. Black-Scholes d2: d2 = d1 - σ√T
7. Call Value: C = Se^-qT N(d1) - Ke^-rT N(d2)
8. Put Value: P = Ke^-rT N(-d2) - Se^-qT N(-d1)
9. One-Sigma Move: Expected move ≈ S × σannual × √T
It estimates historical volatility from a sequence of stock prices, annualizes that volatility, and then applies it to an option pricing model for quick planning insights.
Higher volatility usually increases option value because larger price swings raise the chance of favorable outcomes before expiration.
Log returns are common in quantitative work because they aggregate cleanly over time. Simple returns are easier to explain and interpret quickly.
Use 252 for daily trading days, 52 for weekly data, and 12 for monthly data. Match the number to your sampling period.
No. This tool estimates historical volatility from past prices. Implied volatility comes from current option market prices instead.
More time usually gives the stock more opportunity to move, which often increases time value and changes the theoretical option price.
Yes. It helps you compare compensation packages by showing how uncertain an option grant may be under different volatility assumptions.
No. These are educational estimates based on past prices and model assumptions. Real markets, liquidity, vesting, and taxes can change outcomes.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.