arbitragelab.optimal_mean_reversion.heat_potentials

Module Contents

Classes

HeatPotentials

This class implements the algorithm for finding
class HeatPotentials

This class implements the algorithm for finding profit-taking and stop-loss levels for p/l that follow an Ornstein-Uhlenbeck process using the heat potential method. The following implementation is based on the work of Alexandr Lipton and Marcos Lopez de Prado “A closed-form solution for optimal mean-reverting trading strategies”<https://ssrn.com/abstract=3534445>`_

fit(ou_params: list, delta_grid: float, max_trade_duration: float = None)

Fits the steady-state distribution to the given OU model, assigns the grid density with respect to t, maximum duration of the trade. Calculates and assigns values for optimal stop-loss and profit-taking levels.

Parameters:

  • ou_params – (list) Parameters of the OU model. [theta, mu, sigma]

  • delta_grid – (float) Grid density with respect to t.

  • max_trade_duration – (float) Maximum duration of the trade.

description() → pandas.Series

Returns the statistics of the model. The optimal thresholds are converted back to the terms of the original data.

Returns:

(pd.Series) Summary data for model parameters and optimal levels.

v(max_trade_duration: float) → numpy.ndarray

Calculates the grid of v(t) functions for t in [0,max_trade_duration] (p.5 and p.8)

Parameters:

max_trade_duration – (float) Maximum duration of the trade.

Returns:

(np.array) Grid of v(t).

static upsilon(max_trade_duration: float) → float

Calculates the helper function that corresponds to v(0). (p.5)

param max_trade_duration:

(float) Maximum duration of the trade.

return:

(float) Calculated value of v(0).

omega(max_trade_duration: float) → float

Calculates helper value for a method of heat potentials. (p.5)

Parameters:

max_trade_duration – (float) Maximum duration of the trade.

Returns:

(float) The result of function calculation.

sharpe_calculation(max_trade_duration: float, optimal_profit: float, optimal_stop_loss: float) → float

Calculates the Sharpe ratio. (p.6 )

Parameters:

  • max_trade_duration – (float) Maximum duration of the trade.

  • optimal_profit – (float) Optimal profit-taking threshold.

  • optimal_stop_loss – (float) Optimal stop-loss level.

Returns:

(float) Sharpe ratio.

optimal_levels() → list

Calculates optimal profit-taking and stop-loss levels by maximizing the Sharpe ratio.

Returns:

(list) The list that consists of profit-taking level, stop-loss level, max Sharpe values.