Derivatives Analytics with Python: Data Analysis, Models, Simulation, Calibration and Hedging

CHAPTER 14 Executive Summary

This book is about the market-based valuation of European and American stock index options. It is a discipline of particular interest in derivatives analytics. To this end, it introduces—among a number of basic tools and approaches—the general market model from Bakshi-Cao-Chen (cf. Bakshi et al. (1997)) as a framework to accomplish the following goals:

• modeling market risks: the model should account for market risks generally affecting index options, like index level risk, volatility risk, jump risk and interest rate risk
• efficient valuation of vanilla options: as a major requirement, the market model should be able to value plain vanilla options, like European puts or calls on an index, in an efficient manner; as it turns out, the Fourier transform method in combination with numerical integration or Fast Fourier Transforms (FFT) offers a convenient approach to accomplish this
• calibration of model parameters: equipped with efficient techniques for the valuation of plain vanilla options, the model can then be calibrated to observed market quotes of such instruments in order to derive a single martingale measure for the valuation of other (exotic) index derivatives
• valuation by simulation: in general, numerical methods are necessary to value the majority of (exotic) equity derivatives; Monte Carlo simulation (MCS) is the most flexible one with the Least-Squares Monte Carlo (LSM) algorithm (cf. Longstaff and Schwartz (2001)) allowing for the incorporation ...