Answer-first summary for fast verification
Answer: 59.4%.
## Explanation In the Black-Scholes-Merton model, the probability that a call option expires in the money is given by **N(d₂)**. From the provided table: - **N(d₂) = 0.594** - This translates to **59.4%** **Key Points:** - N(d₂) represents the risk-neutral probability that the call option will finish in-the-money - d₂ is calculated as: d₂ = d₁ - σ√T - For a non-dividend-paying stock, this probability is directly given by N(d₂) - The other values in the table: - N(d₁) = 0.687 is used in the call option pricing formula - N(−d₁) and N(−d₂) are used for put option calculations Therefore, the correct answer is **59.4%**.
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An analyst gathers the following Black–Scholes–Merton option valuation model outputs for a call option on a non-dividend-paying stock:
| Output | Value |
|---|---|
| d₁ | 0.488 |
| d₂ | 0.238 |
| N(d₁) | 0.687 |
| N(d₂) | 0.594 |
| N(−d₁) | 0.313 |
| N(−d₂) | 0.406 |
The probability that the call option expires in the money is:
A
40.6%.
B
48.8%.
C
59.4%.
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