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%

Question

Quizplus · Accepted Answer

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!

The Implied Volatilities for Strike Prices of 1