Question

A three-step binomial tree with terminal stock prices being 1.103, 0.875, 0.695, and 0.552. At time 0, if you have the insider information that at the maturity the stock price will be 0.875. Then, will the option premium at time 0 still be same as if you don't have this information, please choose from the answers below?

A. Yes. Option premium is irrelevant to the private information (about the underlying) that option holder possesses.

B. No. As in that case, the risk neutral probability of the impossible sample paths become zero.

Answer 1

The binomial option valuation model is based on the no-arbitrage approach to valuation. The model as given in the name itself is used to value the option in consideration.

Given the situation that we already know the stock price and the counterparty does not, the option if valued using the binomial theorem will have a particular option premium derived from the model.

If writing the option, the calculated option premium will be the expected premium to be received even if the person knows the final value. If buying the option, the calculated option premium from the binomial model, will have to paid.

Hence, Option A is the correct one. Irrespective of the insider information, an option premium in line with value derived from the binomial model will exist on the call/put option.