Derivatives Portfolios

From a portfolio perspective, a “relevant market” is mainly composed of the relevant risk

factors (underlyings) and their correlations, as well as the derivatives and derivatives

positions, respectively, to be valued. Theoretically, we are now dealing with a general

market model ℳ as defined in Chapter 15, and applying the Fundamental Theorem of

Asset Pricing (with its corollaries) to it.

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The Class

A somewhat complex Python class implementing a portfolio valuation based on the

Fundamental Theorem of Asset Pricing — taking into account multiple relevant risk

factors and multiple derivatives positions — is presented as Example 18-2. The class is

rather comprehensively documented inline, especially during passages that implement

functionality specific to the purpose at hand.

Example 18-2. A class to value a derivatives portfolio

DX Library Portfolio

derivatives_portfolio.py

import numpy as np
import pandas as pd

from dx_valuation import *

models available for risk factor modeling

models = {‘gbm’ : geometric_brownian_motion,
‘jd’ : jump_diffusion,
‘srd’ : square_root_diffusion}

allowed exercise types

otypes = {‘European’ : valuation_mcs_european,
‘American’ : valuation_mcs_american}

class derivatives_portfolio(object):
”’ Class for building portfolios of derivatives positions.

            Attributes

            ==========

            name    :   str

                            name    of  the object

            positions   :   dict

                            dictionary  of  positions   (instances  of  derivatives_position    class)

            val_env :   market_environment

                            market  environment for the valuation

            assets  :   dict

                            dictionary  of  market  environments    for the assets

            correlations    :   list

                            correlations    between assets

            fixed_seed  :   Boolean

                            flag    for fixed   rng seed



            Methods

            =======

            get_positions   :

                            prints  information about   the single  portfolio   positions

            get_statistics  :

                            returns a   pandas  DataFrame   object  with    portfolio   statistics

            ”’

def init(self, name, positions, val_env, assets,
correlations=None, fixed_seed=False):
self.name = name
self.positions = positions
self.val_env = val_env