Value Option with Forward Volatilities

Your question is very unclear, are these 5 different vanilla options? If so just use the given volatility associated with each of the maturities, t_1, t_2, t_3... to find their prices. Unless you are trying to find the price of an option one year from now, that expires in two years from now I don't see why you would need to use forward volatilities.

Or are you perhaps saying that t_2 = 27,45% is the 1-year forward volatility beginning at year 1 (i.e from year 1-2)? If so then you would perhaps use that with the volatility t_1 volatility to find the average yearly volatility for the period year 0-2 in order to value the option with maturity in 2 years from now.

Again, I think you need to clarify your question if you want a proper answer.

If you are referring to an option that is traded in 2015, and its payoff is determined by the spot every year in 2016, 2017, to 2019, e.g. Bermudan payoff

• You need a model that can capture the dynamics of volatility, with a reasonable forward skew

• Local volatility will be a good start

• Known issues: spot/vol corr too high, no vol-of-vol, fwd skew too flat

• What model you use depends on what level of accuracy you want to achieve here