Reading 57: valuing a derivative using a one period binomial model

Question 1

To construct a one-period binomial model for valuing an option, are probabilities of an up-move or a down-move in the underlying price required?
No.
Yes, but they can be calculated from the returns on an up-move and a down-move.
Yes, the model requires estimates for the actual probabilities of an up-move and a down-move.

Answer 1

A one-period binomial model can be constructed based on replication and no-arbitrage pricing, without regard to the probabilities of an up-move or a down-move. (LOS 57.a)

Question 2

In a one-period binomial model based on risk neutrality, the value of an option is best described as the present value of:
a probability-weighted average of two possible outcomes.
a probability-weighted average of a chosen number of possible outcomes.
one of two possible outcomes based on a chosen size of increase or decrease.

Answer 2

In a one-period binomial model based on risk-neutral probabilities, the value of an option is the present value of a probability-weighted average of two possible option payoffs at the end of a single period, during which the price of the underlying asset is assumed to move either up or down to specific values. (LOS 57.b)

Question 3

A one-period binomial model for option pricing uses risk-neutral probabilities because:
the model is based on a no-arbitrage relationship.
they are unbiased estimators of the actual probabilities.
the buyer can let an out-of-the-money option expire unexercised.

Answer 3

Because a one-period binomial model is based on a no-arbitrage relationship, we can discount the expected payoff at the risk-free rate. (LOS 57.b)