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Instructor
Fredrick Michael, Instructor - Financial Derivatives

Fredrick Michael

Dynamic, energetic, self motivated leader, and expert in data analysis whether for financial markets (stocks, bonds, derivatives, commodities FX) or business econometrics and decision systems, or other area of strong expertise of physical sciences (physics , chemistry ) with theory/analysis modeling and simulations, experimental prototyping and laboratory from concept to prototype and to commercial product. Dr. F. Michael is a former US Navy nuclear engineer 1986-1992, a commercial nuclear industry senior level Health Physics consultant. He earned his masters in physics in 1998 (AMO atomic molecular optical) and his Ph.D. in theoretical physics of condensed matter and complex statistical systems in 2002 from UCF the University of Central Florida, with 10 years+ of experience as an NSF National Science Foundation postdoc, fellow of the Advanced Materials center Florida, US government scientist NIST National Institute of Standards and technology chemistry group and the MML materials measurement laboratory, as a charter member and fellow of the US nano-sciences center for theory and computation, as corporate fellow of Kraft Foods NanoTek consortium and PMUSA Philip Morris INEST interdisciplinary network of emerging science and technology. Additionally, as senior scientist at UCSD the University of California drug discovery / bio-molecular chemistry group Skaggs School of Pharmaceutical Sciences and recent awardee of senior fellow of TAU nano-sciences institute...Expertise in nano-materials for energy environment and medicine...expertise in nanometer scale electronics devices, molecular wires, sensors, spectroscopic, logic gates, & solar thermal materials, etc. from modeling/simulation to laboratory synthesis fabrication and characterization.
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Instructor: Fredrick Michael

The course presents in detail the traditional and modern sophisticated derivations, techniques and computing methods utilized to mathematically describe & quantify, which are furthermore used to successfully apply trading of these financial instruments.

  • Get an introduction to the world of financial mathematics as typified by financial derivatives.
  • Hedging strategies & various derivatives uses.
  • Instructor works at NASA MSFC Marshall Space Flight Center as a scientist & production engineer and has a Ph.D. & an M.Sc. from the University of Central Florida.

Duration: 2h 05m

Course Description

This course describes and examines financial derivatives such as forwards, futures and options. Drawing on real world financial markets experience and applications, and from classical texts and publications of impact and these innovative in the field. We review the original motivations for the creation, use of such financial instruments, & discuss the various instruments and strategies in real markets. We then present the financial mathematics of the evolution of such financial derivatives. In detail, we present the derivation of mathematical formula that describes generally derivatives & specifically address issues inherent to European style options, floating strike options, and early exercise uncertainty in American style options. From a wealth portfolio level of description to the trajectory of a random increment & the statistics of the underlying asset the derivative is written on. We present in detail the traditional and modern sophisticated derivations, techniques and computing methods utilized to mathematically describe & quantify, and which are furthermore used to successfully apply trading of these financial instruments. The course material is intended to be supplemented by published materials and with freeware applications written in say Spreadsheets, Matlab, or the .nb Mathematica 'notebook' languages etc. these readily available, and where interest regarding a particular presented topic may inspire further inquiry by the inquisitive.

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What am I going to get from this course?

  • Introduction to the world of financial mathematics as typified by financial derivatives
  • Hedging strategies & various derivatives uses. Introduction In Detail. 
  • A brief review of financial markets & uncertainty. 
  • Statistics & statistical distributions & their properties. 
  • The rxpected value of an observable <x(t)>, as the statistically weighted sum or integral. 
  • Deriving statistics from information theoretic arguments. The observable as  information. 
  • Deriving the equations of temporal evolution of the probability density functions PDFs of statistics. How to obtain the PDEs partial differential equations of evolution of the statistical distributions a.k.a. the PDFs probability density functions.
  • Deriving the stochastic differential equations SDEs of the PDEs partial differential equations. The meaning of 'equivalent descriptions at the micro & macro evolution levels. 
  • The portfolio of assets & derivatives & the maximization of its efficiency. The Black-Scholes equation, a backwards Fokker-Planck type PDE.
  • The European Style Black-Scholes equation. 
  • The European Style options Valuated by Alternative methods.
  • The American Style option. 
  • Solving the American Style option early exercise problem discrete & continuous models & computation

Prerequisites and Target Audience

What will students need to know or do before starting this course?

The 'student' should have a reasonable grasp at least of statistics, calculus I, & some experience with power-series &/or partial differential equations. Stochastic calculus would
be beneficial. Additionally, as much of modern mathematical finance is computational, familiarity with “a” programming language &/or computational statistical software is desirable. However, it should be noted that very sophisticated software & computational tools are readily available to all persons regularly utilizing financial derivatives for real world trading. Additionally, this course is designed to be mostly self-contained, with only a few external resources mostly in the form of additional references & information resources required for actual mastery.

Who should take this course? Who should not?

Anyone who has the prerequisites.

Curriculum

Module 1: Introduction to the world of financial mathematics as typified by financial derivatives

Lecture 1 Forwards, Futures & Options
Lecture 2 Financial Derivatives
Lecture 3 Example Charts
Lecture 4 The Futures Contract

Module 2: Hedging strategies & Various Derivatives Uses. Introduction In Detail

Lecture 5 Hedging
Lecture 6 The Long (purchased) Straddle:

Module 3: A Brief Review Of Financial markets & Uncertainty

Lecture 7 A Brief Review of Financial markets & Uncertainty.
Lecture 8 Individual Risk Preference Variability
Lecture 9 Model Uncertainties and Risk
Lecture 10 Systematic & Deterministic Trends
Lecture 11 Trends: Short Term & Long Term
Lecture 12 Deriving the stochastic differential equations SDEs of the PDEs partial differential equations.
Lecture 13 Stochastic Calculus
Lecture 14 Trajectory Statistics and Microscopic Evolution
Lecture 15 The European Style Options Valuated By Alternative Methods.
Lecture 16 The Portfolio
Lecture 17 Solving the American Style Option Early Exercise Problem

Module 4: The Greeks

Lecture 18 The Greeks

Module 5: Discrete & Continuous Models & Computation

Lecture 19 Discrete Models of Options

Module 6: Advanced Topics In Financial Derivatives

Lecture 20 Computational Numerical Modelling