Answer-first summary for fast verification
Answer: 9.34%
## Explanation **C is correct.** There are two interpolations to be made to find the correct reference implied volatility: one for time (7 months) and one for the K/S₀ ratio (1.075). ### Step-by-step calculation: 1. **Time interpolation between 6 months and 1 year:** - For K/S₀ = 1.05: 9.10 + 1/6 × (9.55 - 9.10) = 9.10 + 0.075 = 9.175 - For K/S₀ = 1.10: 9.45 + 1/6 × (9.75 - 9.45) = 9.45 + 0.05 = 9.50 2. **K/S₀ ratio interpolation between 1.05 and 1.10:** - Since 1.075 is exactly halfway between 1.05 and 1.10: - (9.175 + 9.50) / 2 = 9.3375 ≈ 9.34% ### Why other options are incorrect: - **A (9.18%):** Uses only time interpolation at K/S₀ = 1.05 - **B (9.28%):** Uses only K/S₀ interpolation at 6 months - **D (9.65%):** Uses only K/S₀ interpolation at 1 year This demonstrates how volatility surfaces are used to price options by interpolating both across time and strike price dimensions.
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A market-maker on the foreign exchange (FX) desk at an investment bank has been asked to provide a quote for an FX call option that expires in 7 months. The option has a strike price (K) to spot price (S₀) ratio of 1.075. The market-maker references the following implied volatility surface when creating the quote:
| Time to expiration | Strike price to spot price ratio (K/S₀) |
|---|---|
| 0.90 | |
| 1 month | 9.25 |
| 3 months | 9.10 |
| 6 months | 9.45 |
| 1 year | 9.65 |
What implied volatility should the market-maker use to create the quote?
A
9.18%
B
9.28%
C
9.34%
D
9.65%