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

Which statement about the Black-Scholes formula for a European call is correct?

The price depends on volatility, which is unobservable and must be estimated from data or implied from traded option prices. The share's expected return and investors' risk preferences do not enter the formula because of risk-neutral valuation.

  1. AThe price depends on the expected return of the share, which must be estimated
  2. BThe price depends on investors' risk aversion through the share's beta
  3. CThe price depends on the volatility, which is not directly observable and must be estimated or impliedCorrect
  4. DThe price is independent of the time to expiry
  5. The price requires the share price to be normally rather than lognormally distributed

Explanation

Inputs are share price, strike, time, risk-free rate and volatility. Volatility cannot be observed directly, so it is estimated from history or implied from market prices. The expected return and risk aversion do not enter because of risk-neutral valuation.

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