Let's start by explaining our website name Complex Hamiltonian Systems. A Complex System is just a system with lots of interacting components. The murmuration of a flock of starlings in flight is an example of a Complex System, where individual birds appear to fly randomly in zigzag paths but the flock as a whole has a continuous, rolling boundary. Hamilton was a famous Irish mathematician who developed a way of describing the evolution of systems in time now known as Hamiltonians. Putting this all together, we call our website Complex Hamiltonian Systems because it describes many interacting traders in a market and how their market evolves with time. We call the mathematics we have developed the Volatility Response Model (VRM) which is explained in more detail below.

On a typical trading platform for foreign exchange, there is a huge amount of choice: at least 10 chart types, 25 technical tools, 25 drawing tools and 10 pattern types. To choose between these requires a lot of experience and knowledge. This is the motivation for developing the VRM.

Candlestick charts have been used to trade since the 17th century, when Japanese traders used them for rice contracts. The Volatility Response Model (VRM) calculates the constant mathematical relationship between the candlesticks in one time period and the next. This relationship does not change over time. On this website you can download future VRM predictions for 14 different FX pairs that span tomorrow and the current week.

The VRM is a mathematical function called a Hamiltonian. It describes the market of traders who together form a Complex System. In the diagram below, the letter H is the Hamiltonian that relates one candlestick to the next. The Hamiltonian H never alters between all the historic data and the next candlestick in the future. So find the Hamiltonian H from all the historic data and then work out the next candlestick in the future.

The VRM starts with as much historic daily high, low and close data as possible, going back more than 15 years. From this, the next future day's high, low and close are calculated. We call these H1, L1 and S1. Now, what to make of the future predicted S1? Is this the predicted close at the end of the next day? It turns out that S1 is the sentiment level that lasts throughout the next day. Above S1 the market is bullish. Below S1 the market is bearish.

Now take the daily data and combine them in pairs to create high, low and close data for 2 day candlesticks. Repeat the mathematics and obtain a prediction for the high, low and close for the next 2 days. We call this H2, L2 and S2. Once again S2 turns out to be the sentiment level of the market throughout the next 2 days.

Now repeat the process by creating historic data for 3 day candlesticks, 4 day candlesticks.... and so on.

We repeat the mathematics out to 8 days into the future using 8 day historic candlestick data. This gives us H8, L8 and S8. In all we have 24 levels. That is eight H levels, eight L levels and eight S levels.

The process we just described can be applied to weekly high, low and close data as well. There is no difference in the mathematics. We still end up with 24 levels: eight H levels, eight L levels and eight S levels. This time, however, H1, L1 and S1 describes one week into the future, and H8, L8 and S8 predict for an 8 week period.

The VRM calculates the high, low and sentiment levels up to 8 time periods into the future, either 8 days or 8 weeks, but these predictions will only last for either one day or one week respectively. Once the day or week is completed, the algorithm is used again for the next day and week.

Interestingly, the same levels from the previous period can be calculated in the next time period except they change their label. For instance, an H1 level might become an S8 level in the next time period. Often the VRM levels calculated for yesterday do a good job of describing the price action today. Similarly, the VRM predictions calculated for last week do a good job of describing the price action for this week.

The eight future sentiment levels at both the daily and weekly timescales calculated by the VRM algorithm are very important.

The daily sentiment levels steer the short term trend of the market and the weekly sentiment levels steer the long term trend of the market.

When an FX market becomes bullish in the short term, its price will rise above the highest daily sentiment level and this level will become a support level. Vice versa, when an FX market becomes bearish in the short term, its price will fall below the lowest daily sentiment. When the FX price action is trapped within the daily sentiment levels, this indicates that in the short term the FX market cannot agree on a trend direction at the 8 different timescales.

Similarly, when an FX market becomes bullish in the long term, its price will rise above the highest weekly sentiment level and this level will become a support level. Vice versa, when an FX market becomes bearish in the long term, its price will fall below the lowest weekly sentiment. When the FX price action is trapped within the weekly sentiment levels, this indicates that in the long term the FX market cannot agree on a trend direction at the 8 different timescales.

The final predictions of the VRM are a short term trend channel on a daily timescale and a long term trend channel on a weekly timescale. The short term trend channel interacts with the long term trend channel. They can bounce off each other.

The short term trend channel is steered by the 8 daily sentiment levels and the long term trend channel is steered by the 8 weekly sentiment levels.

The 24 daily levels, 24 weekly levels, short term trend channel and long term trend channel are prices at which foreign exchange prices retrace and reverse. Placed on a trading chart, you can see these retracements and reversals happening at these VRM levels as the market evolves into the future. In summary, financial markets do not move randomly, but move about the levels calculated by the VRM. **The VRM provides a road map or obstacle course through which the future price action will move.** Click on the link below to see how the VRM levels are charted and used in practice.