Python for Finance

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.^[60] 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 ...