advanced-algorithmic-trading

406
if all(self.latest_prices > -1.0):
# Create the observation matrix of the latest prices
# of TLT and the intercept value (1.0) as well as the
# scalar value of the latest price from IEI
F = np.asarray([self.latest_prices[0], 1.0]).reshape((1, 2))
y = self.latest_prices[1]
# The prior value of the states \theta_t is
# distributed as a multivariate Gaussian with
# mean a_t and variance-covariance R_t
if self.R is not None:
self.R = self.C + self.wt
else:
self.R = np.zeros((2, 2))
# Calculate the Kalman Filter update
# ----------------------------------
# Calculate prediction of new observation
# as well as forecast error of that prediction
yhat = F.dot(self.theta)
et = y - yhat
# Q_t is the variance of the prediction of
# observations and hence \sqrt{Q_t} is the
# standard deviation of the predictions
Qt = F.dot(self.R).dot(F.T) + self.vt
sqrt_Qt = np.sqrt(Qt)
# The posterior value of the states \theta_t is
# distributed as a multivariate Gaussian with mean
# m_t and variance-covariance C_t
At = self.R.dot(F.T) / Qt
self.theta = self.theta + At.flatten() * et
self.C = self.R - At * F.dot(self.R)
Finally we generate the trading signals based on the values of e t and √ Q t . To do this we
need to check what the "invested" status is - either "long", "short" or "None". Notice how we
need to adjust the cur_hedge_qty current hedge quantity when we go long or short as the slope
θt 0 is constantly adjusting in time:
# Only trade if days is greater than a "burn in" period
if self.days > 1:
# If we’re not in the market...
if self.invested is None:
if e < -sqrt_Q:
# Long Entry