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Answer: 9.34%
The correct answer is C, 9.34%. To determine the implied volatility for the FX call option with a 7-month expiration and a strike price to spot price ratio (K/So) of 1.075, the market-maker must perform two interpolations: one for time and one for the K/So ratio. The reference implied volatility surface provides volatilities for different time periods and K/So ratios. First, interpolate between the 6-month (9.10% and 9.45%) and 1-year (9.55% and 9.75%) volatilities for the K/So ratios of 1.05 and 1.10, respectively. To do this, calculate the increase in volatility for each time period and apply the proportion for the additional month (7 months - 6 months = 1 month). This results in: - For the 1.05 K/So ratio: 9.10% + (1/6 * (9.55% - 9.10%)) = 9.175% - For the 1.10 K/So ratio: 9.45% + (1/6 * (9.75% - 9.45%)) = 9.5% Since the option's K/So ratio of 1.075 is exactly between 1.05 and 1.10, average the two interpolated volatilities: (9.175% + 9.5%) / 2 = 9.3375%, which rounds to 9.34%. This method ensures that the market-maker uses the most relevant implied volatility for pricing the FX call option, taking into account both the time to expiration and the specific K/So ratio.
Author: LeetQuiz Editorial Team
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At an investment firm, an FX trader is responsible for quoting a currency call option that has a 7-month maturity period. The defining characteristic of this option is a strike price that is 1.075 times the current spot price. In order to accurately formulate this quote, the trader relies on the following table of implied volatility data:
| Time to expiration | Strike price to spot price ratio (K/So) | 0.90 | 0.95 | 1.00 | 1.05 | 1.10 |
|---|---|---|---|---|---|---|
| 1 month | 9.25 | 8.55 | 8.05 | 8.70 | 9.45 | |
| 3 months | 9.10 | 8.70 | 8.30 | 8.75 | 9.15 | |
| 6 months | 9.45 | 9.05 | 8.70 | 9.10 | 9.45 | |
| 1 year | 9.65 | 9.50 | 9.35 | 9.55 | 9.75 |
Using the information provided on the implied volatility surface, which implied volatility should the trader select for quoting the currency call option?
A
9.18%
B
9.28%
C
9.34%
D
9.65%
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