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CA Final · Advanced Financial Management · Derivatives Analysis and Valuation

In a one-period binomial model, an analyst values a call using the risk-neutral probability. Suppose the real-world probability of an upward move in the stock is revised from 60% to 40%, while the up and down prices and the risk-free rate stay unchanged. What happens to the model value of the call?

The call value remains unchanged. In the binomial model the option is priced by replication, using the risk-neutral probability derived from the risk-free rate and the up and down factors. The real-world probability of an up move does not enter the calculation, so changing it from 60% to 40% has no effect on the value.

  1. AIt increases, because the stock is more likely to fall
  2. BIt decreases, because the up state is less likely
  3. CIt remains unchanged, because valuation uses risk-neutral probabilitiesCorrect
  4. DIt cannot be determined without knowing the investors' risk aversion

Explanation

The risk-neutral probability p = (1 + r − d)/(u − d) depends only on the risk-free rate and the up and down factors. The real-world probability does not enter it. Both views of the real-world probability therefore give the same replicating portfolio and the same option value, so the call's value does not change.

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