Python and Julia Chapter 3. Multivariate Volatility Models

# Chapter 3. Multivariate Volatility Models

### Python and Julia

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##### Listing 3.1/3.2
import numpy as np
p = p[:,[0,1]]                          # consider first two stocks
y = np.diff(np.log(p), n=1, axis=0)*100 # calculate returns
y[:,0] = y[:,0]-np.mean(y[:,0])         # subtract mean
y[:,1] = y[:,1]-np.mean(y[:,1])
T = len(y[:,0])

##### Listing 3.1/3.2
using CSV, Statistics, DataFrames;
y1 = diff(log.(p[:,1])).*100; # consider first two stocks
y2 = diff(log.(p[:,2])).*100; # convert prices to returns
y1 = y1 .- mean(y1); # subtract mean
y2 = y2 .- mean(y2);
y = hcat(y1,y2);                  # combine both series horizontally
T = size(y,1);                    # get the length of time series


##### EWMA in Python
EWMA = np.full([T,3], np.nan)
lmbda = 0.94
S = np.cov(y, rowvar = False)
EWMA[0,] = S.flatten()[[0,3,1]]
for i in range(1,T):
S = lmbda * S + (1-lmbda) * np.transpose(np.asmatrix(y[i-1]))* np.asmatrix(y[i-1])
EWMA[i,] = [S[0,0], S[1,1], S[0,1]]
EWMArho = np.divide(EWMA[:,2], np.sqrt(np.multiply(EWMA[:,0],EWMA[:,1])))
print(EWMArho)

##### EWMA in Julia
EWMA = fill(NaN, (T,3))
lambda = 0.94
S = cov(y)                                        # initial (t=1) covar matrix
EWMA[1,:] = [S, S, S]                    # extract var and covar
for i in 2:T                                      # loop though the sample
S = lambda*S + (1-lambda)*y[i-1,:]*(y[i-1,:])'
EWMA[i,:] = [S, S, S]                # convert matrix to vector
end
EWMArho = EWMA[:,3]./sqrt.(EWMA[:,1].*EWMA[:,2]);  # calculate correlations


##### OGARCH in Python


##### OGARCH in Julia



##### DCC in Python


##### DCC in Julia
using ARCHModels, Plots;
dcc = fit(DCC{1, 1, GARCH{1, 1}}, y; meanspec = NoIntercept);
H = covariances(dcc);
DCCrho = [correlations(dcc)[i][1,2] for i = 1:T];
plot(DCCrho, title = "Correlations", legend = false)


##### Correlation comparison in Python


##### Correlation comparison in Julia



##### Financial Risk Forecasting
Market risk forecasting with R, Julia, Python and Matlab. Code, lecture slides, implementation notes, seminar assignments and questions.