
Answer-first summary for fast verification
Answer: 0.40.
The risk-neutral probability (π) is a key concept in binomial option pricing, calculated as: \[ π = \frac{(1 + r) - R_d}{R_u - R_d} \] where: - \( r \) is the risk-free rate (5% or 0.05), - \( R_u \) is the expected up move factor (1 + 0.25 = 1.25), - \( R_d \) is the expected down move factor (1 - 0.25 = 0.75). Substituting the values: \[ π = \frac{(1 + 0.05) - 0.75}{1.25 - 0.75} = 0.60 \] This represents the risk-neutral probability of an **increase** in the underlying price. The probability of a **decrease** is therefore: \[ 1 - π = 1 - 0.60 = 0.40 \] Thus, the correct answer is **B (0.40)**.
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