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CFA Level I · CFA Level I Exam · Valuing a Derivative Using a One-Period Binomial Model

In the one-period binomial model, a call option can be replicated by combining the underlying with borrowing or lending at the risk-free rate. The replication is most likely possible because:

Replication works because there are only two possible states, so a portfolio of the underlying and a risk-free loan or deposit can be chosen to match the option's payoff in both. No-arbitrage then sets the option price equal to that portfolio's cost.

  1. Athe option's payoff in both states can be matched by a portfolio of two instrumentsCorrect
  2. Binvestors are assumed to be risk averse and require a premium
  3. Cthe underlying is assumed to pay a dividend each period

Explanation

With only two states, a position in the underlying and a risk-free bond has two degrees of freedom, so it can match the option payoff in both states. No-arbitrage then sets the option value equal to the portfolio cost. Risk aversion and dividends are not required.

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