Using Random-Walk Maximal Curves to Estimate Price-Move Probabilities

Summary

The note explains a maximal curve as a way to estimate the probability that price reaches a specified distance up or down within a given time. It describes converting a volatility estimate, expressed as price movement per hour, into probabilities with a probability density function based on a random-walk model. Those probabilities can inform the likelihood of stop-loss or profit-target levels being touched over the chosen horizon.

The document gives no empirical validation or worked numerical example; it points to an external article and spreadsheet. Its main caveat is that historical volatility may not represent future volatility, so the resulting probabilities are conditional estimates rather than reliable forecasts. It also suggests using the time horizon to decide whether to exit when neither target is reached, but does not specify how to set that margin or test the exit rule.

Key ideas

• A maximal curve estimates the probability of reaching a price distance within a specified period.
• The described calculation uses volatility as input to a random-walk probability density function.
• Estimated move probabilities can help assess whether stop-loss or profit-target levels may be reached.
• Historical volatility may differ from future volatility, limiting the usefulness of the estimates.

Tags

# What is a maximal curve?


# What is a maximal curve?












I came across the term maximals in this article. Can someone explain what a maximal curve is and how you would calculate it?

## Answer by rupweb (score 0, accepted)

https://quant.stackexchange.com/a/28079

The article says: Taking the volatility as input these curves will tell me the probability of a maximum price (either up or down) being reached.

Using standard deviation of price data a volatility is calculated into a pips per hour number. That's nice. Based on that calculation the "maximal" gives probabilities that a market moves a particular distance over a particular time.

You calculate the maximal using a probability density function. That article uses a random walk function and has a spreadsheet you can download.

Therefore this "maximal" can be used as a probability for stops and profit targets being hit, because they are set a certain distance away from a current price.

The problem is historical volatility is not a guide to future volatility.

I guess what you could do is get into a trade, set your stops and targets for a particular time using these maximals, and if they aren't hit - given a margin for error - you take profit anyway because the calculations were "wrong".

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.