Notes01 - FRE 6083 - Quantitative Methods in Finance...

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FRE 6083 - Quantitative Methods in Finance Frederick Novomestky, Ph.D. 2 FRE 6083- Quantitative Methods in Finance - Copyright F. Novomestky 2007 Course Objectives The first part of this course focuses on the art and science of building models of processes that occur in finance, economics, and the social sciences in general. These may include models of aggregate economic activity or the behavior of asset prices. We do not attempt to cover the spectrum of model types and modeling methodologies; rather, the focus is on models that can be expressed in equation form, relating variables quantitatively. The primary focus is on the use of calculus, linear algebra and probability 3 FRE 6083- Quantitative Methods in Finance - Copyright F. Novomestky 2007 Course Objectives Data are then used to estimate the parameters of the equation or equations, and theoretical relationships are tested statistically. Software tools like Excel and R are used for empirical work. R is a language and environment for statistical computing and graphics. It is a GNU project (e.g., Open Source) which is similar to the S-Plus language developed at Bell Laboratories. Download version from www.r-project.org
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4 FRE 6083- Quantitative Methods in Finance - Copyright F. Novomestky 2007 Course Objectives The second half of the course develops the theory of discrete- and continuous-time stochastic models as applied to the valuation of options and other derivative securities. Brownian motion, Markov chains, Markov process, Poisson process and related stochastic processes, stochastic integration, Itô's formula, and other aspects of stochastic calculus are treated with substantial rigor. 5 FRE 6083- Quantitative Methods in Finance - Copyright F. Novomestky 2007 Course Objectives This includes the derivation and solution of the differential equation leading up to the Black- Scholes model for pricing stocks. The theory is balanced with concrete numerical applications. Basic Monte Carlo simulation techniques will be used in additional to analytical methods. 6 FRE 6083- Quantitative Methods in Finance - Copyright F. Novomestky 2007 Textbooks and Grading Textbooks and Software É Nefcti, Mathematics of Financial Derivatives É Ross, Probability Models É Papoulis, Probability and Random Processes É R Grading É 30% Midterm É 30% Final É 10% Classroom Participation É 30% Homework
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7 FRE 6083- Quantitative Methods in Finance - Copyright F. Novomestky 2007 The Axioms of Probability Set Theory Probability Space Conditional Probabilities and Independent Events 8 FRE 6083- Quantitative Methods in Finance - Copyright F. Novomestky 2007 Set Theory A review of notation and basic set theoretic options is covered in the file SetTheoryReviewSlides.pdf. 9 FRE 6083- Quantitative Methods in Finance - Copyright F. Novomestky 2007 Probability Spaces Definitions Trials The Axioms of Probability Fields Events Definition of an Probability Space Construction of Probability Spaces Probabilities on the Real Line
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10 FRE 6083- Quantitative Methods in Finance - Copyright F. Novomestky 2007 Probability Spaces - Definition A probability space is an ordered triple.
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This note was uploaded on 02/16/2011 for the course FE 6083 taught by Professor Neveskyi during the Spring '11 term at NYU Poly.

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Notes01 - FRE 6083 - Quantitative Methods in Finance...

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