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?)