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Estimating Historical Option Prices from Underlying Prices

Article Quant Q&A · Author: mr_js
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Summary

The document raises whether daily historical option prices can be approximated from historical closing prices of the underlying asset. It identifies Black–Scholes as one possible pricing framework and notes that the model requires implied volatility for accurate valuation. The central issue is that implied volatility is inferred from option market prices, while historical underlying prices alone provide a different input: realized volatility over a selected past window.

No answer or estimation procedure is included, so the document does not establish a method for reconstructing historical option prices. Any estimate based on historical prices would need assumptions about volatility, rates, dividends, contract terms, and the volatility surface, and would not necessarily match observed prices. The prompt is therefore useful as a statement of the data and model limitation, but offers no empirical evidence or worked example.

Key ideas

  • Black–Scholes valuation requires volatility as an input.
  • Historical underlying prices can be used to estimate realized volatility, but they do not directly reveal implied volatility.
  • Underlying prices alone are insufficient to reconstruct actual historical option prices without additional assumptions and contract data.
  • The document poses the estimation question but provides no answer or tested method.

Tags

OptionsDerivatives pricingVolatility
Full text
# How to calculate approximate historical price of options?


# How to calculate approximate historical price of options?












Assuming that I have access to the historical daily closing price, it is possible to approximately calculate the daily price of an option? I understand that one pricing model is the Black-Scholes model. However this requires implied volatility (IV) to get an accurate result. As I understand it, IV cannot be calculated from historical stock prices.

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