Quite Complex Portfolios
========================

This part illustrates that you can **model, value and risk manage quite
complex derivatives portfolios** with DX Analytics.

.. code:: python

    from dx import *
    import time
    import matplotlib.pyplot as plt
    import seaborn as sns; sns.set()
    %matplotlib inline
    np.random.seed(10000)

Multiple Risk Factors
---------------------

The example is based on a **multiple, correlated risk factors**, all
(for the ease of exposition) ``geometric_brownian_motion`` objects.

.. code:: python

    mer = market_environment(name='me', pricing_date=dt.datetime(2015, 1, 1))
    mer.add_constant('initial_value', 0.01)
    mer.add_constant('volatility', 0.1)
    mer.add_constant('kappa', 2.0)
    mer.add_constant('theta', 0.05)
    mer.add_constant('paths', 100) # dummy
    mer.add_constant('frequency', 'M') # dummy
    mer.add_constant('starting_date', mer.pricing_date)
    mer.add_constant('final_date', dt.datetime(2015, 12, 31)) # dummy
    ssr = stochastic_short_rate('ssr', mer)

.. code:: python

    plt.figure(figsize=(10, 6))
    plt.plot(ssr.process.time_grid, ssr.process.get_instrument_values()[:, :10]);
    plt.gcf().autofmt_xdate()



.. image:: 13_dx_quite_complex_portfolios_files/13_dx_quite_complex_portfolios_7_0.png


.. code:: python

    # market environments
    me = market_environment('gbm', dt.datetime(2015, 1, 1))

.. code:: python

    # geometric Brownian motion
    me.add_constant('initial_value', 36.)
    me.add_constant('volatility', 0.2) 
    me.add_constant('currency', 'EUR')

.. code:: python

    # jump diffusion
    me.add_constant('lambda', 0.4)
    me.add_constant('mu', -0.4) 
    me.add_constant('delta', 0.2)

.. code:: python

    # stochastic volatility
    me.add_constant('kappa', 2.0)
    me.add_constant('theta', 0.3) 
    me.add_constant('vol_vol', 0.5)
    me.add_constant('rho', -0.5)

Using 2,500 paths and monthly discretization for the example.

.. code:: python

    # valuation environment
    val_env = market_environment('val_env', dt.datetime(2015, 1, 1))
    val_env.add_constant('paths', 2500)
    val_env.add_constant('frequency', 'M')
    val_env.add_curve('discount_curve', ssr)
    val_env.add_constant('starting_date', dt.datetime(2015, 1, 1))
    val_env.add_constant('final_date', dt.datetime(2016, 12, 31))

.. code:: python

    # add valuation environment to market environments
    me.add_environment(val_env)

.. code:: python

    no = 50  # 50 different risk factors in total

.. code:: python

    risk_factors = {}
    for rf in range(no):
        # random model choice
        sm = np.random.choice(['gbm', 'jd', 'sv'])
        key = '%3d_%s' % (rf + 1, sm)
        risk_factors[key] = market_environment(key, me.pricing_date)
        risk_factors[key].add_environment(me)
        # random initial_value
        risk_factors[key].add_constant('initial_value',
                                        np.random.random() * 40. + 20.)
        # radnom volatility
        risk_factors[key].add_constant('volatility',
                                        np.random.random() * 0.6 + 0.05)
        # the simulation model to choose
        risk_factors[key].add_constant('model', sm)

.. code:: python

    correlations = []
    keys = sorted(risk_factors.keys())
    for key in keys[1:]:
        correlations.append([keys[0], key, np.random.choice([-0.1, 0.0, 0.1])])
    correlations[:3]




.. parsed-literal::

    [['  1_sv', '  2_gbm', 0.10000000000000001],
     ['  1_sv', '  3_gbm', -0.10000000000000001],
     ['  1_sv', '  4_gbm', -0.10000000000000001]]



Options Modeling
----------------

We model a certain number of **derivative instruments** with the
following major assumptions.

.. code:: python

    me_option = market_environment('option', me.pricing_date)
    # choose from a set of maturity dates (month ends)
    maturities = pd.date_range(start=me.pricing_date,
                               end=val_env.get_constant('final_date'),
                               freq='M').to_pydatetime()
    me_option.add_constant('maturity', np.random.choice(maturities))
    me_option.add_constant('currency', 'EUR')
    me_option.add_environment(val_env)

Portfolio Modeling
------------------

The ``derivatives_portfolio`` object we compose consists of **multiple
derivatives positions**. Each option differs with respect to the strike
and the risk factor it is dependent on.

.. code:: python

    # 5 times the number of risk factors
    # as portfolio positions/instruments
    pos = 5 * no              

.. code:: python

    positions = {}
    for i in range(pos):
        ot = np.random.choice(['am_put', 'eur_call'])
        if ot == 'am_put':
            otype = 'American single'
            payoff_func = 'np.maximum(%5.3f - instrument_values, 0)'
        else:
            otype = 'European single'
            payoff_func = 'np.maximum(maturity_value - %5.3f, 0)'
        # random strike
        strike = np.random.randint(36, 40)
        underlying = sorted(risk_factors.keys())[(i + no) % no]
        name = '%d_option_pos_%d' % (i, strike)
        positions[name] = derivatives_position(
                            name=name,
                            quantity=np.random.randint(1, 10),
                            underlyings=[underlying],
                            mar_env=me_option,
                            otype=otype,
            payoff_func=payoff_func % strike)

.. code:: python

    # number of derivatives positions
    len(positions)




.. parsed-literal::

    250



Portfolio Valuation
-------------------

First, the derivatives portfolio with **sequential valuation**.

.. code:: python

    port = derivatives_portfolio(
                    name='portfolio',
                    positions=positions,
                    val_env=val_env,
                    risk_factors=risk_factors,
                    correlations=correlations,
                    parallel=True)  # sequential calculation

.. code:: python

    port.val_env.get_list('cholesky_matrix')




.. parsed-literal::

    array([[ 1.        ,  0.        ,  0.        , ...,  0.        ,
             0.        ,  0.        ],
           [ 0.1       ,  0.99498744,  0.        , ...,  0.        ,
             0.        ,  0.        ],
           [-0.1       ,  0.01005038,  0.99493668, ...,  0.        ,
             0.        ,  0.        ],
           ..., 
           [-0.1       ,  0.01005038, -0.01015242, ...,  0.99239533,
             0.        ,  0.        ],
           [ 0.        ,  0.        ,  0.        , ...,  0.        ,
             1.        ,  0.        ],
           [ 0.1       , -0.01005038,  0.01015242, ...,  0.01526762,
             0.        ,  0.99227788]])



The call of the ``get_values`` method to **value all instruments**.

.. code:: python

    %time res = port.get_statistics(fixed_seed=True)


.. parsed-literal::

    Totals
    pos_value    10327.477405
    pos_delta      115.001400
    pos_vega      8778.425900
    dtype: float64
    CPU times: user 849 ms, sys: 9.15 s, total: 10 s
    Wall time: 31.3 s


.. code:: python

    res.set_index('position', inplace=False)




.. raw:: html

    <div>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>name</th>
          <th>quantity</th>
          <th>otype</th>
          <th>risk_facts</th>
          <th>value</th>
          <th>currency</th>
          <th>pos_value</th>
          <th>pos_delta</th>
          <th>pos_vega</th>
        </tr>
        <tr>
          <th>position</th>
          <th></th>
          <th></th>
          <th></th>
          <th></th>
          <th></th>
          <th></th>
          <th></th>
          <th></th>
          <th></th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>94_option_pos_38</th>
          <td>94_option_pos_38</td>
          <td>9</td>
          <td>European single</td>
          <td>[ 45_sv]</td>
          <td>11.689901</td>
          <td>EUR</td>
          <td>105.209109</td>
          <td>6.5340</td>
          <td>31.3659</td>
        </tr>
        <tr>
          <th>184_option_pos_37</th>
          <td>184_option_pos_37</td>
          <td>3</td>
          <td>American single</td>
          <td>[ 35_jd]</td>
          <td>2.659000</td>
          <td>EUR</td>
          <td>7.977000</td>
          <td>-0.4491</td>
          <td>33.9000</td>
        </tr>
        <tr>
          <th>187_option_pos_36</th>
          <td>187_option_pos_36</td>
          <td>1</td>
          <td>European single</td>
          <td>[ 38_gbm]</td>
          <td>0.035181</td>
          <td>EUR</td>
          <td>0.035181</td>
          <td>0.0215</td>
          <td>1.2782</td>
        </tr>
        <tr>
          <th>181_option_pos_38</th>
          <td>181_option_pos_38</td>
          <td>6</td>
          <td>European single</td>
          <td>[ 32_jd]</td>
          <td>10.185577</td>
          <td>EUR</td>
          <td>61.113462</td>
          <td>4.4790</td>
          <td>57.4704</td>
        </tr>
        <tr>
          <th>22_option_pos_38</th>
          <td>22_option_pos_38</td>
          <td>8</td>
          <td>American single</td>
          <td>[ 23_jd]</td>
          <td>1.136000</td>
          <td>EUR</td>
          <td>9.088000</td>
          <td>-0.5248</td>
          <td>64.0000</td>
        </tr>
        <tr>
          <th>103_option_pos_36</th>
          <td>103_option_pos_36</td>
          <td>2</td>
          <td>European single</td>
          <td>[  4_gbm]</td>
          <td>0.068706</td>
          <td>EUR</td>
          <td>0.137412</td>
          <td>0.1276</td>
          <td>7.2696</td>
        </tr>
        <tr>
          <th>201_option_pos_38</th>
          <td>201_option_pos_38</td>
          <td>3</td>
          <td>American single</td>
          <td>[  2_gbm]</td>
          <td>4.859000</td>
          <td>EUR</td>
          <td>14.577000</td>
          <td>-1.2135</td>
          <td>42.9000</td>
        </tr>
        <tr>
          <th>144_option_pos_39</th>
          <td>144_option_pos_39</td>
          <td>9</td>
          <td>European single</td>
          <td>[ 45_sv]</td>
          <td>11.177332</td>
          <td>EUR</td>
          <td>100.595988</td>
          <td>6.4188</td>
          <td>31.9941</td>
        </tr>
        <tr>
          <th>203_option_pos_38</th>
          <td>203_option_pos_38</td>
          <td>5</td>
          <td>European single</td>
          <td>[  4_gbm]</td>
          <td>0.019660</td>
          <td>EUR</td>
          <td>0.098300</td>
          <td>0.1115</td>
          <td>7.7775</td>
        </tr>
        <tr>
          <th>155_option_pos_39</th>
          <td>155_option_pos_39</td>
          <td>5</td>
          <td>American single</td>
          <td>[  6_jd]</td>
          <td>15.146000</td>
          <td>EUR</td>
          <td>75.730000</td>
          <td>-4.0440</td>
          <td>13.5000</td>
        </tr>
        <tr>
          <th>146_option_pos_36</th>
          <td>146_option_pos_36</td>
          <td>3</td>
          <td>European single</td>
          <td>[ 47_sv]</td>
          <td>2.894735</td>
          <td>EUR</td>
          <td>8.684205</td>
          <td>1.2897</td>
          <td>2.9382</td>
        </tr>
        <tr>
          <th>46_option_pos_39</th>
          <td>46_option_pos_39</td>
          <td>2</td>
          <td>European single</td>
          <td>[ 47_sv]</td>
          <td>2.200646</td>
          <td>EUR</td>
          <td>4.401292</td>
          <td>0.7166</td>
          <td>1.8760</td>
        </tr>
        <tr>
          <th>34_option_pos_37</th>
          <td>34_option_pos_37</td>
          <td>9</td>
          <td>American single</td>
          <td>[ 35_jd]</td>
          <td>2.659000</td>
          <td>EUR</td>
          <td>23.931000</td>
          <td>-1.3473</td>
          <td>101.7000</td>
        </tr>
        <tr>
          <th>188_option_pos_39</th>
          <td>188_option_pos_39</td>
          <td>8</td>
          <td>American single</td>
          <td>[ 39_sv]</td>
          <td>9.770000</td>
          <td>EUR</td>
          <td>78.160000</td>
          <td>-3.9096</td>
          <td>13.7800</td>
        </tr>
        <tr>
          <th>222_option_pos_38</th>
          <td>222_option_pos_38</td>
          <td>4</td>
          <td>European single</td>
          <td>[ 23_jd]</td>
          <td>22.837920</td>
          <td>EUR</td>
          <td>91.351680</td>
          <td>3.5512</td>
          <td>12.6368</td>
        </tr>
        <tr>
          <th>159_option_pos_36</th>
          <td>159_option_pos_36</td>
          <td>9</td>
          <td>American single</td>
          <td>[ 10_sv]</td>
          <td>7.882000</td>
          <td>EUR</td>
          <td>70.938000</td>
          <td>-4.1706</td>
          <td>6.3000</td>
        </tr>
        <tr>
          <th>217_option_pos_39</th>
          <td>217_option_pos_39</td>
          <td>4</td>
          <td>European single</td>
          <td>[ 18_sv]</td>
          <td>13.021438</td>
          <td>EUR</td>
          <td>52.085752</td>
          <td>3.0700</td>
          <td>4.1216</td>
        </tr>
        <tr>
          <th>137_option_pos_39</th>
          <td>137_option_pos_39</td>
          <td>6</td>
          <td>American single</td>
          <td>[ 38_gbm]</td>
          <td>17.842000</td>
          <td>EUR</td>
          <td>107.052000</td>
          <td>-5.9940</td>
          <td>0.6000</td>
        </tr>
        <tr>
          <th>130_option_pos_37</th>
          <td>130_option_pos_37</td>
          <td>1</td>
          <td>European single</td>
          <td>[ 31_sv]</td>
          <td>1.140401</td>
          <td>EUR</td>
          <td>1.140401</td>
          <td>0.2380</td>
          <td>1.2870</td>
        </tr>
        <tr>
          <th>135_option_pos_38</th>
          <td>135_option_pos_38</td>
          <td>2</td>
          <td>European single</td>
          <td>[ 36_gbm]</td>
          <td>18.964940</td>
          <td>EUR</td>
          <td>37.929880</td>
          <td>1.7504</td>
          <td>19.0952</td>
        </tr>
        <tr>
          <th>190_option_pos_36</th>
          <td>190_option_pos_36</td>
          <td>7</td>
          <td>American single</td>
          <td>[ 41_jd]</td>
          <td>5.429000</td>
          <td>EUR</td>
          <td>38.003000</td>
          <td>-2.7216</td>
          <td>79.8000</td>
        </tr>
        <tr>
          <th>109_option_pos_37</th>
          <td>109_option_pos_37</td>
          <td>5</td>
          <td>European single</td>
          <td>[ 10_sv]</td>
          <td>3.839486</td>
          <td>EUR</td>
          <td>19.197430</td>
          <td>2.4440</td>
          <td>6.1185</td>
        </tr>
        <tr>
          <th>191_option_pos_38</th>
          <td>191_option_pos_38</td>
          <td>9</td>
          <td>American single</td>
          <td>[ 42_sv]</td>
          <td>7.267000</td>
          <td>EUR</td>
          <td>65.403000</td>
          <td>-3.6981</td>
          <td>11.7000</td>
        </tr>
        <tr>
          <th>164_option_pos_36</th>
          <td>164_option_pos_36</td>
          <td>4</td>
          <td>European single</td>
          <td>[ 15_gbm]</td>
          <td>5.920606</td>
          <td>EUR</td>
          <td>23.682424</td>
          <td>2.2248</td>
          <td>55.3132</td>
        </tr>
        <tr>
          <th>112_option_pos_37</th>
          <td>112_option_pos_37</td>
          <td>3</td>
          <td>European single</td>
          <td>[ 13_sv]</td>
          <td>1.718209</td>
          <td>EUR</td>
          <td>5.154627</td>
          <td>0.9345</td>
          <td>1.9341</td>
        </tr>
        <tr>
          <th>240_option_pos_36</th>
          <td>240_option_pos_36</td>
          <td>2</td>
          <td>American single</td>
          <td>[ 41_jd]</td>
          <td>5.429000</td>
          <td>EUR</td>
          <td>10.858000</td>
          <td>-0.7776</td>
          <td>22.8000</td>
        </tr>
        <tr>
          <th>39_option_pos_38</th>
          <td>39_option_pos_38</td>
          <td>3</td>
          <td>European single</td>
          <td>[ 40_jd]</td>
          <td>15.213182</td>
          <td>EUR</td>
          <td>45.639546</td>
          <td>2.1216</td>
          <td>35.8626</td>
        </tr>
        <tr>
          <th>233_option_pos_37</th>
          <td>233_option_pos_37</td>
          <td>9</td>
          <td>American single</td>
          <td>[ 34_jd]</td>
          <td>6.746000</td>
          <td>EUR</td>
          <td>60.714000</td>
          <td>-2.0925</td>
          <td>129.9690</td>
        </tr>
        <tr>
          <th>175_option_pos_39</th>
          <td>175_option_pos_39</td>
          <td>7</td>
          <td>American single</td>
          <td>[ 26_gbm]</td>
          <td>3.204000</td>
          <td>EUR</td>
          <td>22.428000</td>
          <td>-1.2404</td>
          <td>95.8629</td>
        </tr>
        <tr>
          <th>37_option_pos_38</th>
          <td>37_option_pos_38</td>
          <td>2</td>
          <td>European single</td>
          <td>[ 38_gbm]</td>
          <td>0.020348</td>
          <td>EUR</td>
          <td>0.040696</td>
          <td>0.0252</td>
          <td>1.6426</td>
        </tr>
        <tr>
          <th>...</th>
          <td>...</td>
          <td>...</td>
          <td>...</td>
          <td>...</td>
          <td>...</td>
          <td>...</td>
          <td>...</td>
          <td>...</td>
          <td>...</td>
        </tr>
        <tr>
          <th>235_option_pos_37</th>
          <td>235_option_pos_37</td>
          <td>4</td>
          <td>American single</td>
          <td>[ 36_gbm]</td>
          <td>0.820000</td>
          <td>EUR</td>
          <td>3.280000</td>
          <td>-0.2464</td>
          <td>36.0000</td>
        </tr>
        <tr>
          <th>11_option_pos_38</th>
          <td>11_option_pos_38</td>
          <td>1</td>
          <td>European single</td>
          <td>[ 12_jd]</td>
          <td>1.310847</td>
          <td>EUR</td>
          <td>1.310847</td>
          <td>0.2786</td>
          <td>8.6502</td>
        </tr>
        <tr>
          <th>15_option_pos_37</th>
          <td>15_option_pos_37</td>
          <td>5</td>
          <td>European single</td>
          <td>[ 16_gbm]</td>
          <td>1.684895</td>
          <td>EUR</td>
          <td>8.424475</td>
          <td>1.5800</td>
          <td>53.0640</td>
        </tr>
        <tr>
          <th>162_option_pos_37</th>
          <td>162_option_pos_37</td>
          <td>9</td>
          <td>American single</td>
          <td>[ 13_sv]</td>
          <td>11.671000</td>
          <td>EUR</td>
          <td>105.039000</td>
          <td>-6.5502</td>
          <td>39.6000</td>
        </tr>
        <tr>
          <th>179_option_pos_39</th>
          <td>179_option_pos_39</td>
          <td>2</td>
          <td>European single</td>
          <td>[ 30_gbm]</td>
          <td>12.171664</td>
          <td>EUR</td>
          <td>24.343328</td>
          <td>1.3514</td>
          <td>29.9058</td>
        </tr>
        <tr>
          <th>104_option_pos_36</th>
          <td>104_option_pos_36</td>
          <td>2</td>
          <td>American single</td>
          <td>[  5_gbm]</td>
          <td>3.937000</td>
          <td>EUR</td>
          <td>7.874000</td>
          <td>-0.4282</td>
          <td>27.1214</td>
        </tr>
        <tr>
          <th>31_option_pos_38</th>
          <td>31_option_pos_38</td>
          <td>9</td>
          <td>European single</td>
          <td>[ 32_jd]</td>
          <td>10.185577</td>
          <td>EUR</td>
          <td>91.670193</td>
          <td>6.7185</td>
          <td>86.2056</td>
        </tr>
        <tr>
          <th>96_option_pos_36</th>
          <td>96_option_pos_36</td>
          <td>3</td>
          <td>American single</td>
          <td>[ 47_sv]</td>
          <td>9.187000</td>
          <td>EUR</td>
          <td>27.561000</td>
          <td>-1.7361</td>
          <td>4.5000</td>
        </tr>
        <tr>
          <th>19_option_pos_36</th>
          <td>19_option_pos_36</td>
          <td>8</td>
          <td>American single</td>
          <td>[ 20_jd]</td>
          <td>12.316000</td>
          <td>EUR</td>
          <td>98.528000</td>
          <td>-8.0000</td>
          <td>13.6000</td>
        </tr>
        <tr>
          <th>87_option_pos_36</th>
          <td>87_option_pos_36</td>
          <td>6</td>
          <td>American single</td>
          <td>[ 38_gbm]</td>
          <td>14.845000</td>
          <td>EUR</td>
          <td>89.070000</td>
          <td>-5.9514</td>
          <td>-3.6000</td>
        </tr>
        <tr>
          <th>121_option_pos_36</th>
          <td>121_option_pos_36</td>
          <td>7</td>
          <td>European single</td>
          <td>[ 22_sv]</td>
          <td>8.149622</td>
          <td>EUR</td>
          <td>57.047354</td>
          <td>4.6865</td>
          <td>19.7043</td>
        </tr>
        <tr>
          <th>200_option_pos_37</th>
          <td>200_option_pos_37</td>
          <td>8</td>
          <td>European single</td>
          <td>[  1_sv]</td>
          <td>7.251997</td>
          <td>EUR</td>
          <td>58.015976</td>
          <td>4.9464</td>
          <td>29.2368</td>
        </tr>
        <tr>
          <th>99_option_pos_36</th>
          <td>99_option_pos_36</td>
          <td>4</td>
          <td>European single</td>
          <td>[ 50_gbm]</td>
          <td>7.058561</td>
          <td>EUR</td>
          <td>28.234244</td>
          <td>2.5984</td>
          <td>52.8508</td>
        </tr>
        <tr>
          <th>53_option_pos_37</th>
          <td>53_option_pos_37</td>
          <td>3</td>
          <td>European single</td>
          <td>[  4_gbm]</td>
          <td>0.037188</td>
          <td>EUR</td>
          <td>0.111564</td>
          <td>0.1203</td>
          <td>7.5129</td>
        </tr>
        <tr>
          <th>111_option_pos_37</th>
          <td>111_option_pos_37</td>
          <td>4</td>
          <td>American single</td>
          <td>[ 12_jd]</td>
          <td>11.090000</td>
          <td>EUR</td>
          <td>44.360000</td>
          <td>-2.9284</td>
          <td>43.2000</td>
        </tr>
        <tr>
          <th>204_option_pos_36</th>
          <td>204_option_pos_36</td>
          <td>1</td>
          <td>American single</td>
          <td>[  5_gbm]</td>
          <td>3.937000</td>
          <td>EUR</td>
          <td>3.937000</td>
          <td>-0.2141</td>
          <td>13.5607</td>
        </tr>
        <tr>
          <th>81_option_pos_36</th>
          <td>81_option_pos_36</td>
          <td>3</td>
          <td>European single</td>
          <td>[ 32_jd]</td>
          <td>11.396591</td>
          <td>EUR</td>
          <td>34.189773</td>
          <td>2.3433</td>
          <td>25.3110</td>
        </tr>
        <tr>
          <th>246_option_pos_37</th>
          <td>246_option_pos_37</td>
          <td>4</td>
          <td>European single</td>
          <td>[ 47_sv]</td>
          <td>2.644399</td>
          <td>EUR</td>
          <td>10.577596</td>
          <td>1.6224</td>
          <td>3.8472</td>
        </tr>
        <tr>
          <th>147_option_pos_36</th>
          <td>147_option_pos_36</td>
          <td>1</td>
          <td>American single</td>
          <td>[ 48_sv]</td>
          <td>9.179000</td>
          <td>EUR</td>
          <td>9.179000</td>
          <td>-0.5690</td>
          <td>0.7000</td>
        </tr>
        <tr>
          <th>243_option_pos_38</th>
          <td>243_option_pos_38</td>
          <td>5</td>
          <td>American single</td>
          <td>[ 44_jd]</td>
          <td>4.452000</td>
          <td>EUR</td>
          <td>22.260000</td>
          <td>-1.0335</td>
          <td>72.5000</td>
        </tr>
        <tr>
          <th>83_option_pos_39</th>
          <td>83_option_pos_39</td>
          <td>8</td>
          <td>American single</td>
          <td>[ 34_jd]</td>
          <td>7.775000</td>
          <td>EUR</td>
          <td>62.200000</td>
          <td>-2.1904</td>
          <td>118.8864</td>
        </tr>
        <tr>
          <th>75_option_pos_39</th>
          <td>75_option_pos_39</td>
          <td>6</td>
          <td>European single</td>
          <td>[ 26_gbm]</td>
          <td>24.214688</td>
          <td>EUR</td>
          <td>145.288128</td>
          <td>4.9746</td>
          <td>90.0108</td>
        </tr>
        <tr>
          <th>234_option_pos_37</th>
          <td>234_option_pos_37</td>
          <td>6</td>
          <td>American single</td>
          <td>[ 35_jd]</td>
          <td>2.659000</td>
          <td>EUR</td>
          <td>15.954000</td>
          <td>-0.8982</td>
          <td>67.8000</td>
        </tr>
        <tr>
          <th>163_option_pos_37</th>
          <td>163_option_pos_37</td>
          <td>5</td>
          <td>European single</td>
          <td>[ 14_jd]</td>
          <td>21.499076</td>
          <td>EUR</td>
          <td>107.495380</td>
          <td>3.9800</td>
          <td>55.7650</td>
        </tr>
        <tr>
          <th>49_option_pos_37</th>
          <td>49_option_pos_37</td>
          <td>4</td>
          <td>American single</td>
          <td>[ 50_gbm]</td>
          <td>4.377000</td>
          <td>EUR</td>
          <td>17.508000</td>
          <td>-1.4884</td>
          <td>62.0000</td>
        </tr>
        <tr>
          <th>110_option_pos_36</th>
          <td>110_option_pos_36</td>
          <td>5</td>
          <td>American single</td>
          <td>[ 11_jd]</td>
          <td>2.080000</td>
          <td>EUR</td>
          <td>10.400000</td>
          <td>-0.7460</td>
          <td>40.5000</td>
        </tr>
        <tr>
          <th>228_option_pos_38</th>
          <td>228_option_pos_38</td>
          <td>3</td>
          <td>European single</td>
          <td>[ 29_jd]</td>
          <td>23.634880</td>
          <td>EUR</td>
          <td>70.904640</td>
          <td>2.5209</td>
          <td>28.7898</td>
        </tr>
        <tr>
          <th>118_option_pos_37</th>
          <td>118_option_pos_37</td>
          <td>8</td>
          <td>American single</td>
          <td>[ 19_gbm]</td>
          <td>6.387000</td>
          <td>EUR</td>
          <td>51.096000</td>
          <td>-2.0376</td>
          <td>122.3936</td>
        </tr>
        <tr>
          <th>150_option_pos_36</th>
          <td>150_option_pos_36</td>
          <td>8</td>
          <td>American single</td>
          <td>[  1_sv]</td>
          <td>7.070000</td>
          <td>EUR</td>
          <td>56.560000</td>
          <td>-2.9960</td>
          <td>26.9624</td>
        </tr>
        <tr>
          <th>124_option_pos_38</th>
          <td>124_option_pos_38</td>
          <td>1</td>
          <td>European single</td>
          <td>[ 25_jd]</td>
          <td>11.170898</td>
          <td>EUR</td>
          <td>11.170898</td>
          <td>0.8039</td>
          <td>6.6341</td>
        </tr>
      </tbody>
    </table>
    <p>250 rows × 9 columns</p>
    </div>



Risk Analysis
-------------

**Full distribution of portfolio present values** illustrated via
histogram.

.. code:: python

    %time pvs = port.get_present_values()


.. parsed-literal::

    CPU times: user 658 ms, sys: 8.02 s, total: 8.68 s
    Wall time: 13.9 s


.. code:: python

    plt.figure(figsize=(10, 6))
    plt.hist(pvs, bins=30);
    plt.xlabel('portfolio present values')
    plt.ylabel('frequency')




.. parsed-literal::

    <matplotlib.text.Text at 0x7f00502b7e10>




.. image:: 13_dx_quite_complex_portfolios_files/13_dx_quite_complex_portfolios_36_1.png


Some **statistics** via pandas.

.. code:: python

    pdf = pd.DataFrame(pvs)
    pdf.describe()




.. raw:: html

    <div>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>0</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>count</th>
          <td>2500.000000</td>
        </tr>
        <tr>
          <th>mean</th>
          <td>10327.480869</td>
        </tr>
        <tr>
          <th>std</th>
          <td>2151.707101</td>
        </tr>
        <tr>
          <th>min</th>
          <td>4691.853004</td>
        </tr>
        <tr>
          <th>25%</th>
          <td>8781.364261</td>
        </tr>
        <tr>
          <th>50%</th>
          <td>10122.550615</td>
        </tr>
        <tr>
          <th>75%</th>
          <td>11584.503917</td>
        </tr>
        <tr>
          <th>max</th>
          <td>20911.950046</td>
        </tr>
      </tbody>
    </table>
    </div>



The **delta** risk report.

.. code:: python

    %%time
    deltas, benchmark = port.get_port_risk(Greek='Delta', fixed_seed=True, step=0.2,
                                           risk_factors=risk_factors.keys()[:4])
    risk_report(deltas)


.. parsed-literal::

    
     19_gbm
    0.8 1.0 1.2 
     24_jd
    0.8 1.0 1.2 
     30_gbm
    0.8 1.0 1.2 
     20_jd
    0.8 1.0 1.2 
    
    
    
     19_gbm_Delta
                 0.8       1.0       1.2
    factor     37.70     47.12     56.54
    value   10234.95  10327.48  10451.53
    
     20_jd_Delta
                 0.8       1.0       1.2
    factor     18.88     23.60     28.32
    value   10403.18  10327.48  10253.94
    
     24_jd_Delta
                 0.8       1.0       1.2
    factor     18.75     23.43     28.12
    value   10400.36  10327.48  10268.91
    
     30_gbm_Delta
                 0.8       1.0       1.2
    factor     32.72     40.90     49.08
    value   10253.47  10327.48  10415.84
    CPU times: user 2.57 s, sys: 6.96 s, total: 9.53 s
    Wall time: 9.84 s


The **vega** risk report.

.. code:: python

    %%time
    vegas, benchmark = port.get_port_risk(Greek='Vega', fixed_seed=True, step=0.2,
                                          risk_factors=risk_factors.keys()[:3])
    risk_report(vegas)


.. parsed-literal::

    
     19_gbm
    0.8 1.0 1.2 
     24_jd
    0.8 1.0 1.2 
     30_gbm
    0.8 1.0 1.2 
    
    
    
     19_gbm_Vega
                 0.8       1.0       1.2
    factor      0.52      0.65      0.78
    value   10249.92  10327.48  10406.17
    
     24_jd_Vega
                 0.8       1.0       1.2
    factor      0.49      0.62      0.74
    value   10295.93  10327.48  10362.83
    
     30_gbm_Vega
                 0.8       1.0       1.2
    factor      0.52      0.65      0.78
    value   10290.69  10327.48  10363.17
    CPU times: user 1.9 s, sys: 7.01 s, total: 8.91 s
    Wall time: 9.13 s


Visualization of Results
------------------------

Selected **results visualized**.

.. code:: python

    res[['pos_value', 'pos_delta', 'pos_vega']].hist(bins=30, figsize=(9, 6))
    plt.ylabel('frequency')




.. parsed-literal::

    <matplotlib.text.Text at 0x7f004afaf9d0>




.. image:: 13_dx_quite_complex_portfolios_files/13_dx_quite_complex_portfolios_45_1.png


**Sample paths** for three underlyings.

.. code:: python

    paths_0 = port.underlying_objects.values()[0]
    paths_0.generate_paths()
    paths_1 = port.underlying_objects.values()[1]
    paths_1.generate_paths()
    paths_2 = port.underlying_objects.values()[2]
    paths_2.generate_paths()

.. code:: python

    pa = 5
    plt.figure(figsize=(10, 6))
    plt.plot(port.time_grid, paths_0.instrument_values[:, :pa], 'b');
    print 'Paths for %s (blue)' % paths_0.name
    plt.plot(port.time_grid, paths_1.instrument_values[:, :pa], 'r.-');
    print 'Paths for %s (red)' % paths_1.name
    plt.plot(port.time_grid, paths_2.instrument_values[:, :pa], 'g-.', lw=2.5);
    print 'Paths for %s (green)' % paths_2.name
    plt.ylabel('risk factor level')
    plt.gcf().autofmt_xdate()


.. parsed-literal::

    Paths for  19_gbm (blue)
    Paths for  24_jd (red)
    Paths for  30_gbm (green)



.. image:: 13_dx_quite_complex_portfolios_files/13_dx_quite_complex_portfolios_48_1.png


**Copyright, License & Disclaimer**

© Dr. Yves J. Hilpisch \| The Python Quants GmbH

DX Analytics (the "dx library") is licensed under the GNU Affero General
Public License version 3 or later (see http://www.gnu.org/licenses/).

DX Analytics comes with no representations or warranties, to the extent
permitted by applicable law.

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