Repricing Options Under Future Volatility Scenarios

Summary

The document poses a scenario-analysis question: how to value a call at a future time while holding the underlying price fixed and changing volatility. It asks whether such future repricing has practical value, and suggests two possible uses: approximating vega from the change in option price relative to the change in volatility, and stress testing. No answer or worked analysis is included, so the note frames a question rather than establishing a method.

The setup leaves important inputs and assumptions unspecified, including how time to expiration and interest rates evolve, and how future volatility scenarios are selected. A price difference across scenarios can illustrate sensitivity, but it should not automatically be treated as a forecast or as a direct hedge ratio; the document does not explain those distinctions. Its value is as a prompt to examine scenario valuation, volatility exposure, and stress testing, with conclusions requiring a fuller pricing framework.

Key ideas

• The question considers repricing a call at future dates while holding the underlying price fixed and changing volatility.
• It proposes comparing price changes with volatility changes as a possible vega estimate.
• It raises stress testing as a potential application but gives no supporting explanation.
• The setup does not specify how time to expiration or other pricing inputs change.
• The document contains no worked example or answer that establishes a practical method.

Tags

# Does it make sense to calculate an option price in future (at t+1)?


# Does it make sense to calculate an option price in future (at t+1)?












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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.