RND/README.md

RND

Recovers the market's own probability distribution from an option chain, using the Breeden-Litzenberger identity.

Companion code for the MQL5 article: https://www.mql5.com/en/articles/23788

What it does

Option prices across strikes encode what the market thinks the distribution of future prices looks like. Breeden-Litzenberger makes that precise: the second derivative of call price with respect to strike is the risk-neutral density.

You cannot differentiate a real chain twice and get anything usable. Strikes are sparse, quotes are noisy, and the second derivative amplifies both into garbage. The article deals with that directly, which is most of the work here.

Once the density is reconstructed it can be read for what the market is pricing, and compared against the realised distribution from historical returns. The gap between the two is the risk premium, which HistoricalDensity.mqh supports.

The chain can come from a CSV or from native MetaTrader 5 options.

Layout

Include/RND/BlackScholes.mqh        pricing, inversion, the forward
Include/RND/RndCore.mqh             density reconstruction
Include/RND/RndData.mqh             chain handling
Include/RND/HistoricalDensity.mqh   realised distribution and risk premium
Include/RND/RndProviderNative.mqh   native MT5 options feed
Indicators/RND/RndProfile.mq5       the density plot
Files/RND/rnd_chain_sample.csv      sample chain
Files/RND/rnd_chain_flatvol.csv     flat-vol chain, as a sanity case

The flat-vol chain is the useful starting point: a known input whose output you can check by eye.

Disclaimer

Educational code. Past behaviour of any model or dataset says nothing about future results. Test on your own data and broker conditions before drawing conclusions.