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IAI Actuarial Core Principles · Economic Modelling · Binomial option-pricing model

Which statement about the no-arbitrage argument used to price options in the binomial model is correct?

The option price equals the cost of the replicating portfolio, so it does not depend on the real-world probability of an up move or on investors' risk preferences. Risk-neutral probabilities are just a computing device and generally differ from real-world probabilities.

  1. AThe option price depends on investors' risk aversion and the real-world up probability
  2. BThe price is the cost of a replicating portfolio, so it is independent of the real-world probability of an up moveCorrect
  3. CThe risk-neutral probability must equal the real-world probability
  4. DThe price must exceed the expected real-world payoff discounted at the risk-free rate
  5. Arbitrage-free pricing requires the share's expected return to equal zero

Explanation

A replicating portfolio of shares and cash has the same payoffs as the option, so its cost is the option price, whatever the real-world probabilities. Risk-neutral probabilities are a computational device and differ from real-world ones in general.

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