Often I ask myself whether it makes sense to calculate the price of a Call at t+1 supposing for example that underlying asset does no move i.e. $S_{t+1} = S_{t}$ and $\sigma$ has changed.

Kind of: $C_{t+1} = f(S_{t}, r, \sigma_{t+1}, K, T)$, $C_{t+2} = f(S_{t}, r, \sigma_{t+2}, K, T)$ etc.

Will that pricing of call in future periods bring any practical value? Where can we use that prices?

I have a few ideas:

  • Possibly as basically that calculation is a prediction of Vega, as $vega = \frac{C_{t+1}-C_{t}}{\sigma_{t+1}-\sigma_{t}}$ it can be used for hedging (not sure about this statement)
  • My professor of trading told me something like "it is used in stress testing" many years ago (what did he talk about?)
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    $\begingroup$ Pricing derivatives at future times is fundamental for pricing valuation adjustments (VA) such as Credit VA, Debit VA, Funding VA, etc. $\endgroup$ – Daneel Olivaw Aug 8 '18 at 12:19
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    $\begingroup$ Overnight risk reports, among other things... I would say: whatever you do in finance, it is important to ask how that changes time-wise and cross-section-wise. $\endgroup$ – stans Aug 8 '18 at 12:36
  • $\begingroup$ @stans what do you mean by "cross-section wise"? $\endgroup$ – Maksym Bondarenko Aug 9 '18 at 18:07

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