elle
(Elle)
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Part III. Derivatives Analytics Library
This part of the book is concerned with the development of a smaller, but nevertheless still
powerful, real-world application for the pricing of options and derivatives by Monte Carlo
simulation.
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The goal is to have, in the end, a set of Python classes — a library we call
DX, for Derivatives AnalytiX — that allows us to do the following:
Modeling
To model short rates for discounting purposes; to model European and American
options, including their underlying risk factors, as well as their relevant market
environments; to model even complex portfolios consisting of multiple options with
multiple, possibly correlated, underlying risk factors
Simulation
To simulate risk factors based on geometric Brownian motions and jump diffusions
as well as on square-root diffusions; to simulate a number of such risk factors
simultaneously and consistently, whether they are correlated or not
Valuation
To value, by the risk-neutral valuation approach, European and American options
with arbitrary payoffs; to value portfolios composed of such options in a consistent,
integrated fashion
Risk management
To estimate numerically the most important Greeks — i.e., the Delta and the Vega of
an option/derivative — independently of the underlying risk factor or the exercise
type
Application
To use the library to value and manage a VSTOXX volatility options portfolio in a
market-based manner (i.e., with a calibrated model for the VSTOXX)
The material presented in this part of the book relies on the DX Analytics library, which is
developed and offered by the author and The Python Quants GmbH (in combination with
the Python Quant Platform). The full-fledged version allows, for instance, the modeling,
pricing, and risk management of complex, multi-risk derivatives and trading books
composed thereof.
The part is divided into the following chapters:
Chapter 15 presents the valuation framework in both theoretical and technical form.
Theoretically, the Fundamental Theorem of Asset Pricing and the risk-neutral
valuation approach are central. Technically, the chapter presents Python classes for
risk-neutral discounting and for market environments.
Chapter 16 is concerned with the simulation of risk factors based on geometric
Brownian motions, jump diffusions, and square-root diffusion processes; a generic
class and three specialized classes are discussed.
