I need suggestions of papers that propose simple and fast methods (not heavily dependent on simulations, nut can depend on simulation) to derive the market implicit probability distribution function of an asset (under risk neutral measure) from plain vanilla option (on this same asset) quoted prices.

I would also appreciate to read the main advantages and drawbacks of each suggested model and a summary of it.

Thank you!


1 Answer 1


The market implied probability density function is $\partial^2 C(K,T) / \partial K^2$, where $C$ is the un discounted option call price. You can also use puts instead of calls for the put part of the smile.

Hence given vanilla options prices (and hence the smile) you need to take the second derivative. Note that you will need to have constructed the full and smooth smile first using interpolation and extrapolation of your preference.

  • $\begingroup$ Could you please suggest some nterpolation and extrapolation methods that are free of arbitrage? That is what I am seeking for. $\endgroup$
    – AnUser
    Commented Oct 24, 2018 at 21:38
  • $\begingroup$ core.ac.uk/download/pdf/6978470.pdf $\endgroup$
    – user34971
    Commented Oct 25, 2018 at 0:45
  • $\begingroup$ would you have the matlab implementation of this procedure? $\endgroup$
    – AnUser
    Commented Oct 25, 2018 at 20:35

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