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Answer: 9.34%
## Explanation To determine the appropriate implied volatility for an FX call option with: - Time to expiration: 7 months - Strike-to-spot ratio (K/S0): 1.075 We need to interpolate from the given volatility surface. ### Step 1: Time Interpolation For K/S0 = 1.05: - 6 months: 9.10% - 1 year: 9.55% Linear interpolation for 7 months: Time difference from 6 months = 1 month Total time difference = 6 months (from 6 months to 1 year) Volatility at 7 months = 9.10% + (1/6) × (9.55% - 9.10%) = 9.10% + 0.075% = 9.175% For K/S0 = 1.10: - 6 months: 9.45% - 1 year: 9.75% Volatility at 7 months = 9.45% + (1/6) × (9.75% - 9.45%) = 9.45% + 0.05% = 9.50% ### Step 2: Strike Ratio Interpolation Now we have: - K/S0 = 1.05 → 9.175% - K/S0 = 1.10 → 9.50% Our target K/S0 = 1.075 is exactly halfway between 1.05 and 1.10. Volatility at K/S0 = 1.075 = (9.175% + 9.50%) / 2 = 9.3375% ≈ 9.34% Therefore, the market-maker should use **9.34%** as the implied volatility for the quote, which corresponds to option **C**.
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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%