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Notebooks on quantitative finance, with interactive python code
Nov 26 2019 20:11
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MoneyScience
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*This is a collection of Jupyter notebooks based on different topics in the area of quantitative finance.*

**Is this a tutorial? **

Almost! :)

This is just a collection of topics and algorithms that in my opinion are interesting.

It contains several topics that are not so popular nowadays, but that can be very powerful. Usually, topics such as PDE methods, Lévy processes, Fourier methods or Kalman filter are not very popular among practitioners, who prefers to work with more standard tools.

The aim of these notebooks is to present these interesting topics, by showing their practical application through an interactive python implementation.

**Who are these notebooks for?**

Not for absolute beginners.

These topics require a basic knowledge in stochastic calculus, financial mathematics and statistics. A basic knowledge of python programming is also necessary.

In these notebooks I will not explain what is a call option, or what is a stochastic process, or a partial differential equation.

However, every time I will introduce a concept, I will also add a link to the corresponding wiki page or to a reference manual. In this way, the reader will be able to immediately understand what I am talking about.

These notes are for students in science, economics or finance who have followed at least one undergraduate course in financial mathematics and statistics.

Self-taught students or practicioners should have read at least an introductiory book on financial mathematics.

### Contents

1.1) **Black-Scholes numerical methods** *(lognormal distribution, change of measure, Monte Carlo, Binomial method)*.

1.2) **SDE simulation and statistics** *(paths generation, Confidence intervals, Hypothesys testing, Geometric Brownian motion, Cox-Ingersoll-Ross process, Euler Maruyama method, parameters estimation)*

1.3) **Fourier inversion methods** *(derivation of inversion formula, numerical inversion, option pricing)*

1.4) **SDE, Heston model** *(correlated Brownian motions, Heston paths, Heston distribution, characteristic function, option pricing)*

1.5) **SDE, Lévy processes** *(Merton, Variance Gamma, NIG, path generation, parameter estimation)*

2.1) **The Black-Scholes PDE** *(PDE discretization, Implicit method, sparse matrix tutorial)*

2.2) **Exotic options** *(Binary options, Barrier options)*

2.3) **American options** *(PDE, Binomial method, Longstaff-Schwartz)*

3.1) **Merton Jump-Diffusion PIDE** *(Implicit-Explicit discretization, discrete convolution, model limitations, Monte Carlo, Fourier inversion, semi-closed formula )*

3.2) **Variance Gamma PIDE** *(approximated jump-diffusion PIDE, Monte Carlo, Fourier inversion, Comparison with Black-Scholes)*

3.3) **Normal Inverse Gaussian PIDE** *(approximated jump-diffusion PIDE, Monte Carlo, Fourier inversion, properties of the Lévy measure)*

4.1) **Pricing with transaction costs** *(Davis-Panas-Zariphopoulou model, singular control problem, HJB variational inequality, indifference pricing, binomial tree, performances)*

5.1) **Linear regression and Kalman filter** *(market data cleaning, Linear regression methods, Kalman filter design, choice of parameters)*

A.1) **Appendix: Linear equations** *(LU, Jacobi, Gauss-Seidel, SOR, Thomas)*

A.2) **Appendix: Code optimization** *(cython, C code)*

A.3) **Appendix: Review of Lévy processes theory** *(basic and important definitions, derivation of the pricing PIDE)*