Category Archives: prediction

So I completed a model and calibration which determines the probability of a price going through a level within a given time period. If one can arrive at a high confidence level, this is incredibly useful for multi-leg execution and as a prop strategy in its own right.

The model uses a SDE with mean reversion, a trend component, and an evolving distribution to determine the price across time. The SDE is evaluated as a monte carlo simulation on a grid. We determine the conditional probability of going from one price level to the next for a given (small) time interval. The sum of the product of the probabilities along the price path represents the posterior probability of being at the given price node at a given time.

With the grid in hand, one can query the grid to determine the probability of a price being above or below a level within a given time, etc. For some markets, we are seeing a 75% confidence level, meaning we are right 3/4 of the time. There were some markets where there was no distinct edge in the approach, I have ideas on how to adjust this, but have not had the time to revisit.

The evolution of the distribution was the most complex to model. Unlike idealized option models, where the distribution is stationary and generally gaussian, the observed intra-day distribution over short periods is neither gaussian nor stationary. We noted that the first 3 or 4 moments have dynamics which can be modelled and fitted on top of an empirical distribution.

The trending and mean reversion functions were fitted using a maximum likelihood estimate, which was easily obtained from the distribution for each time step under given assumptions. The parameters were evolved with a GA to maximize the likelihood.

What is the probable path of a security over the next 1 second, 5 seconds, 30 seconds?

I attended a quantitative algorithmic trading seminar 3 weeks ago where one presenter was discussing fill probability (in general terms). The presenter claimed that their model predicts the price path over the next few minutes to determine how best to read a VWAP strategy.

While I don’t believe it is possible to predict a specific price path, it is possible to determine the probability of any given price path. If we can determine the probability of any given path through time from the current price to some final price in N seconds or minutes, we can compute the expected probability of going through a price level within some period of time.

The expected probability through a node at time Tn at price level Pa on a multinomial tree will simply be the sum of the probability of all sub-paths from Ts to Tn going through Pa. That part may be simple, but accurately determining the likely paths / probabilities is a hard research problem.

Given that the number of paths is exponential with time, the farther out we look the more time it takes to compute a precise expectation. We must use a monte carlo analysis, sampling a calibrated timeseries equation, to approximate the expectation function.

Determining the timeseries function that accurately reflects the market is a very hard research problem. Alas, if I told you my approach would have to kill you 😉