IAI Actuarial Core Principles · Economic Modelling · Binomial option-pricing model
In a one-period binomial model with no arbitrage, which statement about the price of a derivative is correct?
The no-arbitrage derivative price equals the expected payoff under risk-neutral probabilities, discounted at the risk-free rate. It does not depend on real-world probabilities or investor risk aversion, because replication determines the price.
- AIt depends on the real-world probability of an up move
- BIt equals the discounted risk-neutral expectation of its payoffCorrect
- CIt is always the discounted real-world expected payoff
- DIt depends on investors' risk aversion
- It equals the payoff in the up state discounted
Explanation
Replication fixes the price independent of real-world probabilities and risk preferences. It equals the discounted expected payoff under the risk-neutral measure.
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