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This initiative was sparked by the identification of cointegrated pairs, fitting them to an OU process, and devising an optimal strategy based on the OU process—areas that have already been well researched.

I have developed a model for support and resistance:

$$SUP(X_t,\mu_{sup},\theta_{sup}) = X_te^{(\frac{\mu_{sup}}{X_t} -1)\theta_{sup}}$$ $$RES(X_t,\mu_{res},\theta_{res}) = X_te^{(\frac{X_t}{\mu_{res}} -1)\theta_{res}}$$

$$dX_t = SUP(X_t,\mu_{sup},\theta_{sup})dt - RES(X_t,\mu_{res},\theta_{res})dt + X_t\sigma dW_t$$

The idea behind the model: $\mu_{sup}$ represents support line and $\mu_{res}$ represents resistance line. $\theta_{sup}$ and $\theta_{res}$ represents how strong are these levels. $\sigma$ is volatility.

Here is simulation for: $X_0=1,\mu_{sup} = 0.8,\mu_{res}=1.3, \theta_{sup} = \theta_{res} = 4, \sigma= 0.3$

Simulation of resSup process with 20 paths.

Here are my Questions:

  1. Is this an effective method for modeling support and resistance? The use of an exponential function might not be the most suitable approach, as it begins to influence the asset price even before reaching the specified levels. Ideally, we might want a mechanism that activates only after the price crosses the support or resistance thresholds.
  2. How can I construct a statistical test to identify whether the time series exhibits support and resistance levels?
  3. Assuming we have identified a time series that adheres to our SDE model, how can I devise the optimal trading strategy?

PS: I understand that these queries are challenging to address, but I've posed them as a part of a self-imposed exercise/research project.

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