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 ...
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