Suggestions of papers for computing market implied probability distribution function

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!

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.

• Could you please suggest some nterpolation and extrapolation methods that are free of arbitrage? That is what I am seeking for. – AnUser Oct 24 '18 at 21:38