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IAI Actuarial Core Principles · Economic Modelling · Black-Scholes derivative-pricing model

A trader computes the implied volatility of an at-the-money option using Black-Scholes and finds it exceeds the share's recent historical volatility. Which is the most reasonable interpretation?

Implied volatility above historical suggests the market expects greater future volatility or is charging a volatility risk premium. It does not prove mispricing or arbitrage, since implied volatility is forward-looking while historical volatility measures past movement.

  1. AThe option is certainly overpriced and arbitrage exists
  2. BThe market expects future volatility to be higher than recently experienced, or demands a premium for volatility riskCorrect
  3. CBlack-Scholes prices are independent of volatility
  4. DThe share's drift must exceed the risk-free rate
  5. Historical volatility is always the correct forecast

Explanation

Implied volatility is forward-looking, extracted from the market price. It can exceed historical volatility because of expected higher future volatility or a volatility risk premium. This does not by itself indicate arbitrage.

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