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CA Final · Advanced Financial Management · Derivatives Analysis and Valuation

In the binomial option pricing model, an analyst argues that if investors in Arjun Steel are very optimistic, the real-world probability of an up move should be raised, and the call price should therefore rise. Which statement is correct?

The call price is unaffected by the real-world probability of an up move. Binomial pricing relies on a replicating portfolio, so the value depends on the up and down factors and the risk-free rate through the risk-neutral probability, not on investors' subjective beliefs about direction.

  1. AThe call price is unaffected by the real-world up probability, because it depends on the up and down factors and the risk-free rate through the risk-neutral probabilityCorrect
  2. BThe call price rises, because a higher real-world probability raises the expected payoff
  3. CThe call price falls, because the higher expected return is discounted at a higher rate
  4. DThe call price changes only for put options, not for calls

Explanation

The option is priced by replication using the up and down prices and the risk-free rate. The risk-neutral probability, p = (1+r−d)/(u−d), does not contain the investors' subjective probability. Changing optimism without changing u, d or r therefore leaves the price unchanged.

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