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

CHAPTER 3 Market Stylized Facts

3.1 Introduction

In science one often takes the route from the specific to the general—from a number of real world observations to a theory or model describing the phenomenon in general fashion. This chapter therefore mainly conducts an analysis of real world data as a basis for the further modeling and implementation efforts. Our main objects of analysis are the DAX stock index—composed of stocks of large German companies—and European call options on the EURO STOXX 50 stock index—composed of stocks of large European companies.

The chapter first introduces some notions central to equity markets and equity derivatives, like volatility and correlation. It then conducts a simulation study in a laboratory fashion based on the benchmark geometric Brownian motion model of Black-Scholes-Merton (BSM). However, the main part of the chapter is concerned with the analysis of a financial time series of daily DAX index level movements. This is done in a tutorial style where the simplicity and replicability of results (with the provided Python scripts) are the main objectives. The chapter then turns to equity options markets in section 3.5. Here, pricing conventions and practices, the volatility smile/skew and its term structure are the main topics. Section 3.6 then rather briefly takes a look at market realities with regard to short rates.

3.2 Volatility, Correlation and Co.

Volatility may be the most central notion in option and derivatives analytics. There ...