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Inferring Stock Price Probabilities from Call Option Prices

Article Quant Q&A · Author: nxstock-trader
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Summary

The document raises the problem of estimating a stock price probability distribution from call option prices using a procedure attributed to Interactive Brokers. The described approach solves a pair of linear equations at each strike, but the resulting estimates include negative probabilities. The author asks for a simple, robust alternative.

No answers, derivation, diagnostic analysis, or proposed fix are included, so the document does not establish why the estimates become negative or how to construct a reliable distribution. It serves mainly as a concise statement of an options-data inference problem. Any practical use would require additional information about the equations, option quote quality, strike spacing, and assumptions used to translate prices into probabilities.

Key ideas

  • The document describes an attempt to infer a stock price distribution from call option prices.
  • The referenced procedure uses a pair of linear equations at each strike.
  • The estimated probabilities can become negative, raising a question about robustness.
  • No solution, evidence, or validation approach is provided in the document.

Tags

OptionsDerivatives pricingStatistics
Full text
# Compute stock price probability distribution from option data (IB method & negative probabilities issue)


# Compute stock price probability distribution from option data (IB method & negative probabilities issue)












I'm using a procedure as described in the interactive brokers article here (https://www.interactivebrokers.com/en/index.php?f=5910&ns=T) to compute a probability distribution from option (call) prices.

In essence you solve a very simple system of two linear equations at each strike.

The issue is I get negative probabilities coming out of it.

I'm looking for a simple and robust procedure to do this estimation. Thoughts?

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