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CFA Level I · CFA Level I Exam · Pricing and Valuation of Options

When a binomial tree is extended from one period to many periods with shorter steps, the model value of a European option most likely:

With more, shorter steps, the binomial value of a European option converges toward the Black-Scholes-Merton value. Volatility still determines the up and down factors, so it remains a key input, and the risk-neutral approach stays valid at every step.

  1. Abecomes independent of the underlying's volatility
  2. Bconverges toward the value from a continuous-time model such as Black-Scholes-MertonCorrect
  3. Cdiverges because the risk-neutral probabilities change each step

Explanation

As the number of steps rises and step length shrinks, the binomial value for a European option converges toward the Black-Scholes-Merton value. Volatility still drives the up and down factors, and risk-neutral probabilities remain consistent in each step.

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