The correct answer is B (0.46). The risk-neutral probability (π) is a key component in binomial option pricing, ensuring that the discounted expected value of the underlying asset equals its current price. It is calculated using the risk-free rate and the assumed up and down gross returns of the underlying asset:

$π = \frac{(1 + r) - R_d}{R_u - R_d}$

Where:

• $r$ is the risk-free rate (4% or 0.04).
• $R_u$ is the up gross return ($\frac{22}{16} = 1.375$).
• $R_d$ is the down gross return ($\frac{12}{16} = 0.75$).

Substituting the values:

$π = \frac{(1 + 0.04) - 0.75}{1.375 - 0.75} = \frac{0.29}{0.625} = 0.464 ≈ 0.46$

Option A (0.38) is incorrect because it represents the expected return of an upward price move, not the risk-neutral probability. Option C (0.54) is incorrect as it represents the risk-neutral probability of a price decrease (1 - π).