Financial Engineering: Statistical Probabilistic Modeling and Python Investment Modelling Practice

Course 10: Financial Engineering: Statistical Probabilistic Modeling and Python Investment Modelling Practice

I. Course Description

The Stochastic Portfolio Theory (SPT) is a mathematical theory proposed by Robert Fernholz in 2002 to analyze the structure of the stock market and the portfolio behavior. It is descriptive, not normative, and consistent with the observational behavior of the actual market. Standard assumptions, as the basis of early theories such as modern portfolio theory (MPT) and capital asset pricing model (CAPM), do not exist in SPT. The SPT uses continuous-time stochastic processes (especially continuous semimartingales) to represent the price of a single security. Discontinuous processes, such as jumping, are also incorporated into the theory. The theory is a flexible framework for analyzing portfolio behavior and stock market structure. As a practical tool, stochastic portfolio theory has been applied to the analysis and optimization of portfolio performance, and has become the basis of successful investment strategies for more than a decade.

The course introduces the concepts of self-financing transactions, no-arbitrage, and replication pricing in the context of a binary tree model. The no-arbitrage price is expressed as a so-called “risk-neutral” expectation. This makes it possible to calculate arbitrage-free prices and hedging strategies. This course reviews some necessary mathematical concepts, course involves theoretical content include: financial markets and financial derivatives, by flipping a coin to understand the basic probability theory, binary tree model, no arbitrage, self-financing portfolio, replication, derivatives pricing and hedging, multi-period binomial model: pricing and hedging, Asian options and American options.

II. Professor Introduction

Johannes Ruf – Tenured Professor at the London School of Economics

Professor Johannes Ruf is a professor of Mathematics at the London School of Economics. He served as Deputy Director of Teaching at the London School of Mathematics for 2021-2022. His research focuses on the field of stochastic analysis and its applications in mathematical finance. In mathematical finance, he has published articles in several top journals on random portfolio theory, exchange rate options, and modeling of financial markets in the presence of arbitrage. In the stochastic analysis, the professors research mainly focuses on the consistent integrability and one-dimensional diffusion of local martingales. Furthermore, the professors research fields include economic learning models and stochastic approximations, and estimation of social structure using indirectly observed network data.

III. Syllabus

1. Introduction to financial markets and financial derivatives
2. Basic theory of probability theory and Python background knowledge
3. Binomial model (top)
4. Binomial model (bottom)
5. Multi-stage binomial model
6. Exotic options
7. A Monte Carlo simulation method in option pricing
8. Binomial model derived from Black-Scholes
9. 9.Black-Scholes option pricing
10. 10.Black-Scholes Advanced topics