44 lines
1.7 KiB
Markdown
44 lines
1.7 KiB
Markdown
 | # RND
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Recovers the market's own probability distribution from an option chain, using
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the Breeden-Litzenberger identity.
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Companion code for the MQL5 article: https://www.mql5.com/en/articles/23788
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## What it does
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Option prices across strikes encode what the market thinks the distribution of
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future prices looks like. Breeden-Litzenberger makes that precise: the second
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derivative of call price with respect to strike is the risk-neutral density.
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You cannot differentiate a real chain twice and get anything usable. Strikes are
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sparse, quotes are noisy, and the second derivative amplifies both into garbage.
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The article deals with that directly, which is most of the work here.
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Once the density is reconstructed it can be read for what the market is pricing,
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and compared against the realised distribution from historical returns. The gap
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between the two is the risk premium, which `HistoricalDensity.mqh` supports.
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The chain can come from a CSV or from native MetaTrader 5 options.
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## Layout
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```
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Include/RND/BlackScholes.mqh pricing, inversion, the forward
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Include/RND/RndCore.mqh density reconstruction
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Include/RND/RndData.mqh chain handling
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Include/RND/HistoricalDensity.mqh realised distribution and risk premium
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Include/RND/RndProviderNative.mqh native MT5 options feed
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Indicators/RND/RndProfile.mq5 the density plot
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Files/RND/rnd_chain_sample.csv sample chain
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Files/RND/rnd_chain_flatvol.csv flat-vol chain, as a sanity case
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```
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The flat-vol chain is the useful starting point: a known input whose output you
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can check by eye.
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## Disclaimer
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Educational code. Past behaviour of any model or dataset says nothing about
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future results. Test on your own data and broker conditions before drawing
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conclusions.
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