# Modelling option price change in N days

I need to understand how will my option price change if the price of underlying asset changes by, for example, 15% in 30 days. I would like to use BS formula, but in this case I know all parameters except implied volatility. The problem is that IV today will differ from IV in 30 days. How can I model that? Should I use local volatility model?

• what options are you looking at? I imagine you'd need to model the dynamics of implied vol surface if it's exotic. I don't think local vol contains such dynamics. – Will Gu Feb 21 '17 at 18:35
• I am looking at simple call option – Alexandr Proskurin Feb 22 '17 at 9:06
• @WillGu he could price the vanilla option in local vol, and then bucket all the paths across strikes at some future time (30 days), and average each of those. This would be better (i think) than doing something implying price changes from current greeks, and since it's a single option, we don't have to worry about the fact that local vol is poor for forward start options. And you could always just try it again with SLV and see if it makes a difference. – will Jun 22 '17 at 11:43

• Your option price is not linear in the underlying price. Therefore, you can linearize it by a first order taylor expansion: $\Delta P = P_{t+50} - P_t$ can be approximated by $\Delta_{option} \times (S_{t+50} - S_t) + \Upsilon \times (\sigma_{t+50} - \sigma_t$) (with $\Upsilon$ being the vega of your option) for small variations of $\Delta S$ and $\Delta \sigma$. However, if you consider dramatic changes, this approach might not be accurate. – JejeBelfort Feb 23 '17 at 8:57