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FRM Part I · FRM Exam Part I · The Black-Scholes-Merton Model

A stock trades at 50 with no dividends, the risk-free rate is 0%, and a one-year at-the-money call is priced at 3.99. Using the approximation that an at-the-money call is worth about 0.4 x S x sigma x sqrt(T), what implied volatility results, and what is the approximate one-standard-deviation one-year move in the stock implied by it?

Implied volatility is about 20% and the one-standard-deviation annual move is about 10. Setting 3.99 = 0.4 x 50 x sigma x 1 gives sigma of roughly 0.20, and multiplying the stock price of 50 by 20% gives a move of about 10.

  1. AVolatility 20%; move about 10.0Correct
  2. BVolatility 16%; move about 8.0
  3. CVolatility 20%; move about 20.0
  4. DVolatility 8%; move about 4.0

Explanation

3.99 = 0.4 x 50 x sigma x 1 = 20 sigma, so sigma = 0.1995, about 20%. One-standard-deviation move = S x sigma = 50 x 0.20 = 10. Option C confuses volatility in percent with the dollar move. Option B wrongly uses 0.5 x ... style scaling error.

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