Limits of Calibrating Black–Scholes from Strike-Price Quotes Alone

Summary

The document poses an inverse pricing problem: fitting a Black–Scholes model to binary option prices observed across strike prices when the time to maturity, volatility, risk-free rate, and underlying price are all unknown. The stated goal is to predict prices at strikes outside the observed sample, while questioning whether a multi-parameter optimization would produce meaningful parameter estimates.

No answer, model derivation, data description, or calibration results are provided. The question highlights a key modeling challenge: strike-price observations alone may not uniquely identify the inputs needed by Black–Scholes, and fitted parameters may not be economically interpretable. The document does not establish whether out-of-sample prediction is feasible or recommend an alternative method, so it serves as a problem statement rather than a demonstrated calibration procedure.

Key ideas

• The question considers fitting Black–Scholes prices using only strike-price and option-price observations.
• The underlying price, maturity, volatility, and risk-free rate are all unspecified.
• The author questions whether optimizing several unknown parameters would yield meaningful calibration.
• No answer or evidence is supplied to resolve identifiability or out-of-sample prediction.

Tags

# Calibration using only strike price


# Calibration using only strike price












I have a binary option and want to calibrate it's BS pricing model. I only have a series of Strike Price vs the Option price, no knowledge on time to maturity, volatility, risk free rate or the underlying price. I have to predict option price for some out of sample set of strike prices. How would I go about calibration of such a model? Or is there some other approach?

I don't think Multi parameter optimisation makes sense here, no sense finding the optimal risk free rate.

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