Mathematics of the Financial Markets

The book aims to prioritise what needs mastering and presentsthe content in the most understandable, concise and pedagogical wayillustrated by real market examples. Given the variety and thecomplexity of the materials the book covers, the author sortsthrough a vast array of topics in a subjective way, relying uponmore than twenty years of experience as a market practitioner. Thebook only requires the reader to be knowledgeable in the basics ofalgebra and statistics. The Mathematical formulae are only fully proven when the proofbrings some useful insight. These formulae are translated fromalgebra into plain English to aid understanding as the vastmajority of practitioners involved in the financial markets are notrequired to compute or calculate prices or sensitivities themselvesas they have access to data providers. Thus, the intention of thisbook is for the practitioner to gain a deeper understanding ofthese calculations, both for a safety reason - it is betterto understand what is behind the data we manipulate - andsecondly being able to appreciate the magnitude of the prices weare confronted with and being able to draft a rough calculation,aside of the market data. The author has avoided excessive formalism where possible.Formalism is securing the outputs of research, but may, in othercircumstances, burden the understanding by non-mathematicians; anexample of this case is in the chapter dedicated to the basis ofstochastic calculus. The book is divided into two parts: * First, the deterministic world, starting from the yield curvebuilding and related calculations (spot rates, forward rates,discrete versus continuous compounding, etc.), and continuing withspot instruments valuation (short term rates, bonds, currencies andstocks) and forward instruments valuation (forward forex, FRAs andvariants, swaps & futures); * Second, the probabilistic world, starting with the basis ofstochastic calculus and the alternative approach of ARMA to GARCH,and continuing with derivative pricing: options, second generationoptions, volatility, credit derivatives; * This second part is completed by a chapter dedicated to marketperformance & risk measures, and a chapter widening the scopeof quantitative models beyond the Gaussian hypothesis andevidencing the potential troubles linked to derivative pricingmodels.