question archive The stock market volatility over the next month is unknown

The stock market volatility over the next month is unknown

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The stock market volatility over the next month is unknown.

Suppose that the volatility σ will be either: 10% annualized, with probability 70%, or 20% annualized, with probability 30%. What is the “effective” volatility per annum? (In other words, if you are going to use Black-Scholes, what number will you use for σ)?

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Effective volatility = (10% * 70%) + (20%*30%) = 7% + 6% = 13%

effective volatility is 13%