Why Historical Option Prices Require Historical Volatility Surfaces

Summary

The question asks whether past option prices can be reconstructed by applying Black–Scholes to historical underlying prices, increasing time to maturity as dates recede, and recalculating volatility using only information available on each date. The answer stresses a more fundamental data limitation: today’s implied volatility does not reveal the option’s implied volatility in the past.

A credible historical valuation requires market data snapshots from the relevant dates, including the underlying spot price, the forward, and the volatility surface or the volatility for the specific option. The exchange explains why adjusting maturity and recomputing a historical estimate from the underlying alone is insufficient to recover past market prices. It offers no pricing example or detailed procedure, and it addresses historical valuation rather than forecasting or a complete option backtesting methodology.

Key ideas

• Current implied volatility cannot establish an option’s implied volatility on earlier dates.
• Historical option valuation requires contemporaneous market snapshots for the dates being studied.
• Relevant inputs include spot, forward, and the volatility surface or the volatility of the specific option.
• The answer does not provide a reconstruction algorithm or a worked Black–Scholes example.

Tags

# How to produce historical prices of an option?


# How to produce historical prices of an option?












Let's say we have an option with underlying stock X and 2 years until maturity. We work out its volatility from X's historical prices across 3 trading years (756 days). To price the option, I can use Black-Scholes and feed in the parameters - but what if I want to also find the options price on the previous days that we got X's historical prices from?

Am I correct in assuming that every day we go back from today our time to maturity will increase by 1/252 (aka 1 trading day)? Does this mean that we have to recompute the volatility every day we go back to exclude the "future" days?

So day 1 (today) uses our initial time to maturity `T` and volatility; day 2 (yesterday) uses `T-(1/252)` as the time to maturity and recomputes the volatility to exclude day 1; and so on...

Highly appreciate any help, thanks.

## Answer by wchyk-cyw (score 1)

https://quant.stackexchange.com/a/29723

The simple answer is you cannot do that really... There is no plausible way to derive the implied volatility of an option in the past given the IV as of today. You would need an entire set of historical market data snapshot at the time, the spot, forward, vol surface or the vol for the particular option you want to value.

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