Lesson 3 of 6 · All lessons in this module
  1. The lognormal distribution
  2. From continuous returns to lognormal pricesVideo lesson
  3. Estimating and annualising volatility
  4. Monte Carlo simulation: what it is and what it is for
  5. Running a Monte Carlo simulation, step by step
  6. Bootstrap resampling

Lesson 3 of 6 · 12 min

Estimating and annualising volatility

Volatility is the annualised standard deviation of continuously compounded returns, usually estimated from daily prices and scaled up by 250\sqrt{250}.

In short

  • Volatility = the standard deviation of continuously compounded returns, quoted on an annual basis by convention.
  • Recipe: prices → ln⁡(Pt/Pt−1)\ln(P_t/P_{t-1}) → sample standard deviation (divide by n − 1) → multiply by 250\sqrt{250}.
  • 250 is the approximate number of trading days in a year. Weekly data use 52\sqrt{52}; monthly data use 12\sqrt{12}.
  • The daily mean times 250 estimates the expected annual continuous return, but a short sample makes that estimate close to useless.
  • n + 1 prices give only n returns.

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