With clearly explained theory and step-by-step instructions for building and using the equations, this comprehensive toolkit allows quantitative professionals, at all levels, to put derivative pricing and risk controlling models into practice.
Compiled by a leading professor of mathematical finance, Marcello Minenna, this extensive manual will enable you to:
• understand the models adopted by the financial markets;
• evaluate the practical application of these models;
• implement the models presented;
• develop the skills required to independently tailor new models to your own specific needs.
As well as an exhaustive reference guide for advanced practitioners and academics, this accessible manual is also designed for beginners and intermediate users to quickly grasp the complexities of quantitative finance.
This self-contained and methodical guide is all you will need to fully grasp the mathematics underlying the pricing of derivatives. And most importantly, will empower you to put your quantitative skills into practice.

I CALCULUS

1 Set Theory

2 Linear Algebra

3 Sequences and Series

4 Differential Calculus

5 Integral Calculus

6 Remarkable Functions

7 Complex Numbers

8 Differential Equations

9 Transforms

II PROBABILITY

10 Measure Theory

11 Probability Theory

12 Stochastic Calculus

13 Stochastic Differential Equations

III FINANCE

14 Actuarial Calculus

15 Equity Derivatives Models

- Asymptomatic analysis and Portfolio replication

- Martingale and forward measures

- Stochastic and Partial Differential Equation

- Fourier Transform

16 Term-Structure models

- Short rate diffusive processes

- Arbitrage-free conditions

- Stochastic and Partial Differential Equation

- Zero Coupon Bond Price under different measures

INDEX

Marcello Minenna is a senior enforcement officer at CONSOB (the Italian Securities and Exchange Commission) where he is in charge of analysing and developing quantitative models for surveillance.
Marcello has been teaching in the field of financial mathematics in several Italian and foreign universities.
He received his Phd in applied mathematics for social sciences from the State University of Brescia, his MA in mathematics in financefrom Columbia University and his degree in economics from Bocconi University.
His research interests include quantitative models for surveillance and more general areas of finance.