Answer-first summary for fast verification
Answer: the difference between ($101.25×0.45) and ($100×0.41).
## Explanation In the Black model for European call options on futures: **Call price formula**: C = e^(-rT) × [F × N(d₁) - X × N(d₂)] Where: - F = futures price = $101.25 - X = exercise price = $100 - N(d₁) = 0.45 - N(d₂) = 0.41 The term inside the brackets is: F × N(d₁) - X × N(d₂) = $101.25 × 0.45 - $100 × 0.41 This represents the **difference between ($101.25×0.45) and ($100×0.41)**. We then take the present value of this difference using e^(-rT). Therefore, option C is correct.
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| Calls | Puts |
|---|---|
| N(d₁) = 0.45 | N(-d₁) = 0.55 |
| N(d₂) = 0.41 | N(-d₂) = 0.58 |
The exercise price is $100 and the futures contract is priced at $101.25. Using the Black model, the value of a European call on the futures contract is the present value of:
A
the difference between ($100×0.45) and ($101.25×0.41).
B
the difference between ($101.25×0.41) and ($100×0.45).
C
the difference between ($101.25×0.45) and ($100×0.41).
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