Theoretical foundations for quantitative finance

This book provides simple introduction to quantitative finance for students and junior quants who want to approach the typical industry problems with practical but rigorous ambition. It shows a simple link between theoretical technicalities and practical solutions. Mathematical aspects are discussed from a practitioner perspective, with a deep focus on practical implications, favoring the intuition and the imagination. In addition, the new post-crisis paradigms, like multi-curves, x-value adjustments (xVA) and Counterparty Credit Risk are also discussed in a very simple framework. Finally, real world data and numerical simulations are compared in order to provide a reader with a simple and handy insight on the actual model performances.

Machine generated contents note: ch. 1 Introduction -- ch. 2 All the Financial Math You Need to Survive with Interesting Applications -- 2.1.Introduction -- 2.2.Probability Space -- 2.2.1.Probability Measure and Random Variables -- 2.2.2.The Information Flow Through Time: The Role of the Filtration -- 2.3.How to Estimate a Random Variable -- Expectations and Conditioning -- 2.4.Main Features of Probability Measure -- 2.5.Moments and Cumulants -- 2.6.Statistical Estimators -- 2.7.Probability Density Functions -- 2.7.1.Uniform Distribution -- 2.7.2.Bernoulli and Binomial Distributions -- 2.7.3.Normal Distribution -- 2.7.4.Empirical Distribution -- 2.7.5.Exponential Distribution and Student's t-Distribution -- 2.8.Central Limit Theorem -- 2.9.Stochastic Processes -- 2.10.Brownian Motion -- 2.11.Quadratic Variation -- 2.12.Martingale -- 2.13.Stochastic Differential Equations (SDEs) -- 2.14.Ito's Lemma -- 2.15.Some Very Useful Theorems -- 2.15.1.Martingale Representation Theorem --

Note continued: 2.15.2.Feynman-Kac Theorem -- 2.15.3.Radon -- Nikodym Theorem -- 2.15.4.Girsanov's Theorem -- ch. 3 The Pricing of Financial Derivatives -- The Replica Approach -- 3.1.Introduction -- The Pr…