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FRM Part I · FRM Exam Part I · Measuring and Monitoring Volatility

A one-month at-the-money call option on a stock is priced by the market at a level that implies a Black-Scholes-Merton volatility of 30% per year. The stock's historical volatility over the past 60 days is 22% per year. Assuming 252 trading days per year, what is the implied one-day volatility, and how does it compare with the historical one-day volatility (rounded)?

Daily volatility equals annual volatility divided by the square root of 252, about 15.875. The implied 30% gives roughly 1.89% per day, and the historical 22% gives roughly 1.39% per day. Dividing by 252 itself is a common mistake.

  1. AImplied 1.89% per day; historical 1.39% per dayCorrect
  2. BImplied 0.12% per day; historical 0.09% per day
  3. CImplied 30.00% per day; historical 22.00% per day
  4. DImplied 1.89% per day; historical 0.88% per day

Explanation

Daily volatility = annual volatility / sqrt(252) = annual / 15.875. Implied: 30/15.875 = 1.89%. Historical: 22/15.875 = 1.386%, about 1.39%. Dividing by 252 instead of its square root gives the 0.12% and 0.09% distractors; dividing 22 by 25 is not a valid scaling.

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