# Computation of Future Implied Volatility Surface

I do have a question on the future implied volatility surface. The current implied volatility surface is easy to obtain, e.g using some interpolation technique on current options prices.

For computation of the future implied volatility surface, e.g at T=2 years Does anyone have an example of how to obtain this assuming e.g Local vol (dupire) or Heston dynamics?

Thank you!

• perhaps by both methods.. 1. Monte Carlo, 2. PDE – Benedict Oct 11 at 6:48
• Hi @Benedict, devil is in the details: it really depends on what you mean by "future implied volatility surface". One possible approach would be to price forward starts with moneyness $k$, starting date $T_1=2Y$ and various tenors $\tau > 0$ in Monte Carlo i.e. instruments with current price: $$V(k,\tau) = \Bbb{E}_0 \left[ D(0,T_2) \left( \frac{S_{T_2}}{S_{T_1}} - k \right)^+ \right]$$ with $T_2 = T_1 + \tau$, then implying a BS volatility from the prices $V(k,\tau), \forall (k,\tau) \in \mathcal{K} \times \mathcal{T}$. – Quantuple Oct 12 at 8:02
• Hi @Quantuple. Thank you for your reply. I was actually trying to understand how the implied volatility surfaces moves across times (e.g starting from T =0 to T=2), using dupire local vol dynamics or heston stochastic vol dynamics. There is already a way to compute at T=0 implied volatility surface, which is the current time. But I dont know how to arrive at the implied vol surface if i simulate my model to T=2 years from now. – Benedict Oct 12 at 10:27
• What do you assume the spot is at t+2? – will Oct 12 at 14:29
• @will need a little more clues – Benedict 2 days ago