#!/usr/bin/env python
# coding: utf-8

# <img src="http://hilpisch.com/tpq_logo.png" alt="The Python Quants" width="45%" align="right" border="4">

# # Quickstart

# This brief first part illustrates---without much explanation---the usage of the DX Analytics library. It models two risk factors, two derivatives instruments and values these in a portfolio context.

# In[1]:


import dx
import datetime as dt
import pandas as pd
from pylab import plt
plt.style.use('seaborn')


# ## Risk Factor Models

# The first step is to define a **model for the risk-neutral discounting**.

# In[2]:


r = dx.constant_short_rate('r', 0.01)


# We then define a **market environment** containing the major parameter specifications needed,

# In[3]:


me_1 = dx.market_environment('me', dt.datetime(2016, 1, 1))


# In[4]:


me_1.add_constant('initial_value', 100.)
  # starting value of simulated processes
me_1.add_constant('volatility', 0.2)
  # volatiltiy factor
me_1.add_constant('final_date', dt.datetime(2017, 6, 30))
  # horizon for simulation
me_1.add_constant('currency', 'EUR')
  # currency of instrument
me_1.add_constant('frequency', 'W')
  # frequency for discretization
me_1.add_constant('paths', 10000)
  # number of paths
me_1.add_curve('discount_curve', r)
  # number of paths


# Next, the model object for the **first risk factor**, based on the geometric Brownian motion (Black-Scholes-Merton (1973) model).

# In[5]:


gbm_1 = dx.geometric_brownian_motion('gbm_1', me_1)


# Some paths visualized.

# In[6]:


pdf = pd.DataFrame(gbm_1.get_instrument_values(), index=gbm_1.time_grid)


# In[7]:


get_ipython().run_line_magic('matplotlib', 'inline')
pdf.iloc[:, :10].plot(legend=False, figsize=(10, 6));


# **Second risk factor** with higher volatility. We overwrite the respective value in the market environment.

# In[8]:


me_2 = dx.market_environment('me_2', me_1.pricing_date)
me_2.add_environment(me_1)  # add complete environment
me_2.add_constant('volatility', 0.5)  # overwrite value


# In[9]:


gbm_2 = dx.geometric_brownian_motion('gbm_2', me_2)


# In[10]:


pdf = pd.DataFrame(gbm_2.get_instrument_values(), index=gbm_2.time_grid)


# In[11]:


pdf.iloc[:, :10].plot(legend=False, figsize=(10, 6));


# ## Valuation Models

# Based on the risk factors, we can then define derivatives models for valuation. To this end, we need to add at least one (the `maturity`), in general two (`maturity` and `strike`), parameters to the market environments.

# In[12]:


me_opt = dx.market_environment('me_opt', me_1.pricing_date)
me_opt.add_environment(me_1)
me_opt.add_constant('maturity', dt.datetime(2017, 6, 30))
me_opt.add_constant('strike', 110.)


# The first derivative is an **American put option** on the first risk factor `gbm_1`.

# In[13]:


am_put = dx.valuation_mcs_american_single(
            name='am_put',
            underlying=gbm_1,
            mar_env=me_opt,
            payoff_func='np.maximum(strike - instrument_values, 0)')


# Let us calculate a **Monte Carlo present value estimate** and estimates for the option **Greeks**.

# In[14]:


am_put.present_value()


# In[15]:


am_put.delta()


# In[16]:


am_put.gamma()


# In[17]:


am_put.vega()


# In[18]:


am_put.theta()


# In[19]:


am_put.rho()


# The second derivative is a **European call option** on the second risk factor `gbm_2`.

# In[20]:


eur_call = dx.valuation_mcs_european_single(
            name='eur_call',
            underlying=gbm_2,
            mar_env=me_opt,
            payoff_func='np.maximum(maturity_value - strike, 0)')


# Valuation and Greek estimation for this option.

# In[21]:


eur_call.present_value()


# In[22]:


eur_call.delta()


# In[23]:


eur_call.gamma()


# In[24]:


eur_call.vega()


# In[25]:


eur_call.theta()


# In[26]:


eur_call.rho()


# ## Excursion: SABR Model 

# To illustrate how general the approach of DX Analytics is, let us quickly analyze an option based on a SABR stochastic volatility process. In what follows herafter, the SABR model does not play a role.
# 
# We need to define different parameters obviously.

# In[27]:


me_3 = dx.market_environment('me_3', me_1.pricing_date)
me_3.add_environment(me_1)  # add complete environment


# In[28]:


# interest rate like parmeters
me_3.add_constant('initial_value', 0.05)
  # initial value
me_3.add_constant('alpha', 0.1)
  # initial variance
me_3.add_constant('beta', 0.5)
  # exponent
me_3.add_constant('rho', 0.1)
  # correlation factor
me_3.add_constant('vol_vol', 0.5)
  # volatility of volatility/variance


# The model object instantiation.

# In[29]:


sabr = dx.sabr_stochastic_volatility('sabr', me_3)


# The valuation object instantiation.

# In[30]:


me_opt.add_constant('strike', me_3.get_constant('initial_value'))


# In[31]:


sabr_call = dx.valuation_mcs_european_single(
            name='sabr_call',
            underlying=sabr,
            mar_env=me_opt,
            payoff_func='np.maximum(maturity_value - strike, 0)')


# Some statistics --- same syntax/API even if the model is more complex.

# In[32]:


sabr_call.present_value(fixed_seed=True)


# In[33]:


sabr_call.delta()


# In[34]:


sabr_call.rho()


# In[35]:


# resetting the option strike
me_opt.add_constant('strike', 110.)


# ## Options Portfolio

# ### Modeling

# In a portfolio context, we need to add **information about the model class(es)** to be used to the market environments of the risk factors.

# In[36]:


me_1.add_constant('model', 'gbm')
me_2.add_constant('model', 'gbm')


# To compose a portfolio consisting of our just defined options, we need to define **derivatives positions**. Note that this step is *independent* from the risk factor model and option model definitions. We only use the market environment data and some additional information needed (e.g. payoff functions).

# In[37]:


put = dx.derivatives_position(
            name='put',
            quantity=2,
            underlyings=['gbm_1'],
            mar_env=me_opt,
            otype='American single',
            payoff_func='np.maximum(strike - instrument_values, 0)')


# In[38]:


call = dx.derivatives_position(
            name='call',
            quantity=3,
            underlyings=['gbm_2'],
            mar_env=me_opt,
            otype='European single',
            payoff_func='np.maximum(maturity_value - strike, 0)')


# Let us define the **relevant market** by 2 Python dictionaries, the correlation between the two risk factors and a valuation environment.

# In[39]:


risk_factors = {'gbm_1': me_1, 'gbm_2' : me_2}
correlations = [['gbm_1', 'gbm_2', -0.4]]
positions = {'put' : put, 'call' : call}


# In[40]:


val_env = dx.market_environment('general', dt.datetime(2016, 1, 1))
val_env.add_constant('frequency', 'W')
val_env.add_constant('paths', 10000)
val_env.add_constant('starting_date', val_env.pricing_date)
val_env.add_constant('final_date', val_env.pricing_date)
val_env.add_curve('discount_curve', r)


# These are used to define the **derivatives portfolio**.

# In[41]:


port = dx.derivatives_portfolio(
            name='portfolio',  # name 
            positions=positions,  # derivatives positions
            val_env=val_env,  # valuation environment
            risk_factors=risk_factors, # relevant risk factors
            correlations=correlations, # correlation between risk factors
            parallel=False)  # parallel valuation


# ### Simulation and Valuation

# Now, we can get the **position values for the portfolio** via the `get_values` method.

# In[42]:


port.get_values()


# Via the `get_statistics` methods delta and vega values are provided as well.

# In[43]:


port.get_statistics()


# Much more complex scenarios are possible with DX Analytics

# ### Risk Reports

# Having modeled the derivatives portfolio, **risk reports** are only two method calls away.

# In[44]:


deltas, benchvalue = port.get_port_risk(Greek='Delta')


# In[45]:


deltas


# In[46]:


deltas.loc(axis=0)[:, 'value'] - benchvalue


# In[47]:


vegas, benchvalue = port.get_port_risk(Greek='Vega', step=0.05)


# In[48]:


vegas


# In[49]:


vegas.loc(axis=0)[:, 'value'] - benchvalue


# **Copyright, License & Disclaimer**
# 
# © Dr. Yves J. Hilpisch | The Python Quants GmbH
# 
# DX Analytics (the "dx library" or "dx package") 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.
# 
# http://tpq.io | [dx@tpq.io](mailto:team@tpq.io) |
# http://twitter.com/dyjh
# 
# <img src="http://hilpisch.com/tpq_logo.png" alt="The Python Quants" width="35%" align="right" border="0"><br>
# 
# **Quant Platform** | http://pqp.io
# 
# **Python for Finance Training** | http://training.tpq.io
# 
# **Certificate in Computational Finance** | http://compfinance.tpq.io
# 
# **Derivatives Analytics with Python (Wiley Finance)** |
# http://dawp.tpq.io
# 
# **Python for Finance (2nd ed., O'Reilly)** |
# http://py4fi.tpq.io