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IAI Actuarial Core Principles · Economic Modelling · Principles of option pricing

In a binomial option pricing model, which statement about the risk-neutral probability q is correct?

The risk-neutral probability is (1+r-d)/(u-d), and it lies strictly between 0 and 1 only when d < 1+r < u, which is the no-arbitrage condition. It is independent of real-world probabilities, risk preferences and the strike price.

  1. AIt equals the real-world probability of an up-move
  2. BIt must lie between 0 and 1 for no arbitrage to exist, which requires d < 1+r < uCorrect
  3. CIt increases when investors become more risk averse
  4. DIt depends on the strike price of the option
  5. It is the same for calls and puts only if the strike is at the money

Explanation

q = ((1+r) - d)/(u - d) lies strictly between 0 and 1 exactly when d < 1+r < u, the no-arbitrage condition. It does not use real-world probabilities, risk aversion or strike, and it is the same for all derivatives on the share.

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