Financial Derivatives
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The document outlines a comprehensive course on financial derivatives, including forwards, futures, and options, emphasizing their application in real-world financial markets. It delves into mathematical concepts and quantitative methods used to analyze these derivatives, explaining risk management strategies and the mathematical foundations of pricing models like the Black-Scholes equation. Additionally, it highlights the instructor's credentials and experience in financial markets and emphasizes the course's aim to provide a deep understanding of both the theoretical and practical aspects of financial derivatives.
Financial Derivatives
- 2. Financial Markets Derivatives. Fredrick Michael, PhD Scientist (NASA & Experfy)
- 3. Fredrick Michael, PhD Scientist, Data and Analytics • PhD & MSc University of Central Florida. Dual Thesis In Theoretical Physics (PhD) of materials and 2nd in complex and random systems with a focus on financial markets (available online). Published in leading journals on financial markets. Invited speaker international conference(s) on economics and financial mathematics. Real world financial markets trading experience and expertise as well as model development and data analytics. MSc in experimental AMO physics. • Additional Experience: Scientist, NIST National Institute of Standards & Technology. Pittnachioff Quantitative Finance, as the senior Markets & Trading analyst and models development lead. Agathos Scientific, Research. US Patents & Trademarks Office quasi-judicial officer, ‘Patents Examiner’ in Nuclear Engineering, and in Intellectual Property Law. • Current Roles: Experfy Data Institute (non-profit of Experfy inc./Harvard Innovation Lab) Director of Big Data. NASA MSFC Marshall Space Flight Center as a Scientist & production Engineer.
- 4. Course Outline • (I) Introduction to the world of financial mathematics as typified by financial Derivatives. o Forwards, futures & options. What are they, & how did they come about. How & why they are used and (typically) in what (secondary) markets today. What do financial derivatives 'quants' do as participants in such secondary financial markets. o The macroscopic evolution of financial derivatives: forwards, futures & options in terms of profits & losses time horizons. The use of derivatives in 'hedging' strategies. How financial derivatives compare to the concept of 'insurance' and how do they function as 'insurance'. o Financial Markets: Primary & Secondary markets. o Stochastic Trajectories. Increment Histograms. Envelope Functions. o Envelope functions as Statistical density functions i.e. ‘the’ statistics. o Outliers and statistics of real markets. • (II) Forwards, Futures and Options and their profit and loss profiles. o Forwards. o Futures. o Options. • (III) Hedging & Insuring Against Risk. o Derivatives as hedge strategy instruments. o Tax Incentives to Hedge. o The derivative as a mere speculation tool. o The two sided hedges: Straddles, Butterflies & Condors to name a few.
- 5. Course Outline • (IV) Sources of uncertainty & therefore risk. • markets 'global' uncertainty risk. • markets 'local' uncertainty risk. • risk preference variability. • model uncertainties & risk. o Sources of systematic & deterministic trends. • trends, short term & long term. • trend following, the so-called 'herd' mentality & response. • seasonality & economic/markets macro to micro cycles. o Boom & Bust Cycles. • (V) Mathematical Quantification of Uncertainty. o Uncertainty, noise, randomness, open systems. o Random Walks…random variables…stochastic means random+deterministic o Averages of random variables. o Stochastic Processes from Stochastic Trajectories.
- 6. Course Outline o VI) Microscopic Stochastics & Macroscopic Partial Differential Equations and Statistics. • From SDE stochastic differential equations to PDE partial differential equations. • Gaussian & Wiener noise. • How to make a nonlinear noise and nonlinear (coefficients) SDE. • Standard Form Fokker-Planck PDEs as the general PDE of statistics. o VII) The Black-Scholes Equation. o Portfolios and assets in our derivation. o Risk neutral models and the Delta hedge. o The backwards Fokker-Planck type PDE; The Black-Scholes equation. o The Greeks…or the rates of change of various portfolio characteristics from option value to time decay of value and so on. o VIII) Discrete Models of Options. • Types of discrete processes: Binomial, Trinomial and fixed and arbitrary incremental evolution (jumps). • The discrete process taken to the continuous limit is a diffusion Fokker-Planck equation. • The discrete and continuous model options therefore under various bounday conditions and assumptions of coefficients.
- 7. Course Outline o IX) Solutions of the Black-Scholes Equation. • Numerical. • Exact, closed form solutions of the traditional Black-Scholes equation. • Implied volatility, implied SDEs, volatility ‘smiles’. • American style options, the inequality portfolio. o Conclusions. o Bibliography & References.
- 8. What am I going to get from this course? • Description of the course: o 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 describe 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 some detail albeit the introductory, traditional and modern sophisticated derivations, techniques and computing methods utilized to mathematically describe & quantify Derivatives pricing, and which are furthermore used to successfully apply trading of these financial instruments.