# Forward-Start Option Implied Volatility

I am preparing for an interview on Monday and I came across a practice question which has me stumped.

"The implied volatility of a 1 year option is 20% and the implied volatility of a 2 year option on the same underlying is trading at 10%. Estimate the implied volatility of a one year option forward starting in 1 year."

Its basically asking, "what is the annualized volatility the market expects for the second year?" correct?

We can't just do $\frac{0.2 + x}{2} = 0.1$ because volatilities are not additive correct? So we have to convert to variances first. So now its $\frac{0.04 + x}{ 2} = 0.01$, which doesn't make any sense.

• You're correct, total variance should be a monotonic increasing function. – will Nov 19 '16 at 17:22
• The only thing I can think of is you have an interest rate curve that looks really strange, but I still don't think that will do it. – barrycarter Nov 21 '16 at 21:11