Consider a Binomial Tree Setting in Which in Each Period $u > 1$

question 31

Multiple Choice

Consider a binomial tree setting in which in each period the price goes up by $u > 1$ (with probability $p$ ) or down by $d < 1$ (with probability $1 - p$ ) . The risk-free interest rate per time step is zero, so a dollar invested at the beginning of the period returns $R = \$ 1$ at the end of the period. Let $Q$ be the risk-neutral probability of a two-period at-the-money call finishing in-the-money when there are no dividends; and let $Q ^ { D }$ be the risk-neutral probability of a two-period at-the-money call finishing in-the-money when there is a dividend of size $D > 0$ between the first and second periods. Which of the following is most accurate?

• A) \(Q = Q ^ { D }\) always.
• B) \(Q \leq Q ^ { D }\) always.
• C) \(Q \geq Q ^ { D }\) always.
• D) Depending on the parameters \(u\) , \(d\) , and \(D\) , both \(Q > Q ^ { D }\) and \(Q \leq Q ^ { D }\) are possible.

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Definitions:

Utility Function

A mathematical representation in economics that quantifies the satisfaction or happiness that a consumer derives from consuming goods and services.

Budget Constraint

The limitations on the purchase capabilities of an individual or entity, based on their available income and the prices of goods and services.

Income

The amount of money received by an individual or entity in exchange for labor or services, through investments, or from any other sources.

Nuts

Typically refers to dry, edible seeds or fruits with a high fat content, but in economics or general usage, it might not have a specialized meaning beyond its common understanding.