The art of quantitative finance Vol. 2. Volatilities, stochastic analysis and valuation tools (Q6041116)

This book is the second volume of the three-volume series ''\textit{The Art of Quantitative Finance}'', authored by G. Larcher. This second volume starts with an investigation of the concept and the properties of volatility in financial markets, proceeding with the valuation of standard and exotic equity derivatives as well as interest rate derivatives. The contents are organised in three chapters: 1. Volatilities; 2. Extensions on the Black-Scholes theory to other types of options; 3. Stochastic models for interest rates and valuation of interest rate derivatives. The first chapter discusses several properties of volatility, implied volatility, volatility indices and volatility derivatives. This chapter is enriched by several illustrations based on market data and takes the reader on a guided tour through the many facets of volatility modelling in finance. The second chapter analyses several types of exotic payoffs and non-standard options, focusing on numerical methods for option pricing. Finally, the third chapter introduces the basics of stochastic calculus and applies these tools to the valuation of interest rate derivatives in classical models (e.g., Gaussian short rate models, affine models). It is a bit surprising that Chapter 2 (``Extensions of the Black-Scholes theory'') appears before the basics of the Black-Scholes model, which are presented towards the end of the volume. The author's presentation is clear and accessible, focusing more on the intuition than on mathematical abstraction or generality.