The implied volatilities for strike prices of 1.1 and 1.2 when the time to maturity is 6 months are 20% and 22%. The implied volatilities for strike prices of 1.1 and 1.2 when the time to maturity is 1 year are 18.8% and 20.2%
Using linear interpolation, what is the implied volatility for a strike price of 1.12 and a time to maturity of 10 months?
A. 19.24%
B. 19.52%
C. 20.48%
D. 19.96%
B
This involves a two-dimensional interpolation. We can either interpolate between strike prices first and then interpolate between maturities, or the other way round. Suppose we interpolate between strike prices first. We get the implied volatility for a 6-month option with a time to maturity of 6 months and a strike price of 1.12 as 0.8×20+0.2×22=20.4%. Similarly, we get the implied volatility for a 1 year option and a strike price of 1.12 as 0.8×18.8+0.2×20.2=19.08%. We next interpolate between maturities to get the volatility for a 10 month option with a strike price of 1.12 as 0.33× 20.4+0.66×19.08=19.52%. If you chose to interpolate between maturities first and then between strike prices you should have got the same answer!
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