Python for Finance, 2nd Edition

Part V. Derivatives Analytics

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.¹ The goal is to have, in the end, a set of Python classes—a pricing library called DX, for Derivatives analytiX—that allows for 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 motion and jump diffusions as well as on square-root diffusions, and 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 (“global valuation”)

Risk management

To estimate numerically the most important Greeks—i.e., the delta and the vega of an option/derivative—independent of the underlying risk factor or the exercise type

Application

To use the package to value and manage a portfolio of non-traded American options on the DAX 30 stock index in market-consistent fashion; i.e., based on a calibrated ...