Questions About Bondarenko Risk-Neutral Density Convolution Formulas

Summary

The document raises two issues in code for estimating risk-neutral densities with Bondarenko’s positive convolution approximation. First, the paper’s synthetic option price includes terms for contributions from below the listed strike range, but the questioner cannot locate corresponding terms in the code. Second, the question compares competing expressions for a double integral of the density and notes that the implementation appears to use a third expression.

The post does not resolve either issue or provide calculations validating one formula over another. It is useful as a prompt to check boundary contributions when approximating prices over a finite strike grid and to verify integral identities by differentiating them. The material is limited to questions about a particular implementation; it gives no corrected derivation, empirical evidence, or general assessment of the method’s accuracy.

Key ideas

• The questioner is concerned that a synthetic option price formula includes lower-tail terms absent from the code.
• The post identifies a disagreement between the paper’s stated double-integral formula and the questioner’s derivation.
• The implementation is said to use a third expression, whose correctness the post questions.
• No answer or validated correction is provided.

Tags

# question about code posted for calculation of risk neutral density using Bondarenko convolution method


# question about code posted for calculation of risk neutral density using Bondarenko convolution method












I have questions about the code (found here Estimation of Risk-Neutral Densities Using Positive Convolution Approximation - Python).

- The synthetic price in Bondarenko paper includes two terms before the dot product of ak with double integral. These correspond to the double integral left of the listed strike range. I cannot find them in this code.

- Also there is likely a typo in formula Bondarenko gave for double integral he wrote `double integral=density - x * integral of density` I get `double integral = x * integral of density - integral of x* density` the code uses a third expression `double integral = x* integral of density + density`. If you differentiate this or Bondarenko's formula, result doesn't look right. so there may be a typo there as well.

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