Discussing the article: "Recovering Option-Implied Probability Distributions Across Four Markets in MQL5"
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Check out the new article: Recovering Option-Implied Probability Distributions Across Four Markets in MQL5.
A practical route from the option chain to probability levels inside MetaTrader 5. For GLD, SLV, SPY, and USO, the risk-neutral density implied by each ETF's options is recovered with the Breeden-Litzenberger identity and checked for static arbitrage, after the method itself is validated against an analytic lognormal. A Python feed publishes the percentiles; an MQL5 service rescales them onto a related symbol, draws levels, and alerts when price leaves the risk-neutral 5 to 95 percent band. Every reading carries its own diagnostics, and full source is included.
A single number can hide a great deal. Ask the options market how much an instrument might move over the next month, and it answers with one figure, an implied volatility. That figure is informative, and it is also a compression. One number describes a whole set of possible outcomes, and it describes them faithfully only if those outcomes are shaped the way the pricing model assumes.
They are not, and the chain says so. Options struck far below the money trade at higher implied volatilities than options struck at the money, which is another way of saying the market does not believe in the tidy lognormal outcome that one number stands for. On the GLD reading below, the recovered distribution has a kurtosis of 7.4, against 3.1 for a lognormal distribution with the same at-the-money volatility and 3.0 for a normal one.
So, the chain contains more than a single volatility. It also implies a full terminal probability distribution, recoverable from the quoted prices by an identity nearly fifty years old. The output is a set of price levels with a probability attached to each one. I pulled one number out of a chain like this in an earlier article and set it against what the market had actually been doing. Writing it left me with a question I could not drop. That one number assumes a shape for the outcomes, and I wanted to know which shape the chain was actually pricing. I went back to the same data and took the whole distribution instead. It turned out useful enough to keep on my chart, and that is what this is.
The chain that gets read here is GLD, the gold ETF, so what comes out is a distribution of GLD. But the method is not about gold, and the article does not ask you to take that on faith: the same unchanged pipeline is run on SLV, SPY, and USO, on two separate afternoons, and every reading is published with its diagnostics. Their connections to XAUUSD, XAGUSD, US500, and USOIL are proxy mappings for monitoring, not equivalences.
Author: Eugenio Gustavo Guilarte Homayden