Mathematical finance

From Wikipedia, the free encyclopedia

Mathematical finance is the branch of applied mathematics concerned with the financial markets.

The subject has a close relationship with the discipline of financial economics, which is concerned with much of the underlying theory. Generally, mathematical finance will derive, and extend, the mathematical or numerical models suggested by financial economics. Thus, for example, while a financial economist might study the structural reasons why a company may have a certain share price, a financial mathematician may take the share price as a given, and attempt to use stochastic calculus to obtain the fair value of derivatives of the stock.

In terms of practice, mathematical finance also overlaps heavily with the fields of financial engineering and computational finance. Arguably, all three are largely synonymous, although the latter two focus on application, while the former focuses on modelling and derivation; see Quantitative analyst.

Many universities around the world now offer degree and research programs in mathematical finance.

Contents 1 Mathematical finance articles 1.1 Mathematical tools 1.2 Derivatives pricing 2 See also 3 External links 3.1 Resources 3.2 Institutional 3.3 Theory 3.4 Research 3.5 Education 3.6 Training

[edit] Mathematical finance articles

[edit] Mathematical tools

• Calculus
• Differential equation
• Linear algebra
• Numerical analysis
• Real analysis
• Probability
• Probability distribution
  • Binomial distribution
  • Log-normal distribution
• Expected value
• Value at risk
• Risk-neutral measure
• Stochastic calculus
  • Brownian motion
  • Lévy process
• Itô's lemma
• Fourier transform
• Girsanov's theorem
• Radon-Nikodym derivative
• Monte Carlo method
• Partial differential equations
  • Heat equation
• Martingale representation theorem
• Feynman Kac Formula
• Dynkin formula
• Stochastic differential equations
• Volatility
  • ARCH model
  • GARCH model
• Stochastic volatility
• Mathematical model
• Numerical method
  • Numerical partial differential equations
    • Crank-Nicolson method
    • Finite difference method

[edit] Derivatives pricing

• Rational pricing assumptions
  • Risk neutral valuation
  • Arbitrage-free pricing
• Futures
  • Futures contract pricing
• Options
  • Put-call parity (Arbitrage relationships for options)
  • Moneyness
  • Option time value
  • Pricing models
    • Black-Scholes
    • Black model
    • Binomial options model
    • Monte Carlo option model
    • Implied volatility
      • Volatility smile
    • The Greeks
• Interest rate derivatives
  • Short rate model
    • Hull-White model
  • LIBOR Market Model
  • Heath-Jarrow-Morton framework

[edit] See also

• Computational finance
• Financial Engineering
• Derivative (finance), list of derivatives topics
• Modeling and analysis of financial markets
• Fundamental financial concepts - topics
• Model (economics)
• QuantLib Mathematical finance library
• List of finance topics, List of finance topics (alphabetical)
• List of economics topics, List of economists
• List of accounting topics
• List of marketing topics
• List of management topics

[edit] External links

[edit] Resources

• FinMath.com - Chicago Financial Mathematics, Financial Engineering and Risk Management Workshop
• Global Derivatives Quantitative Mathematics Glossary
• Quantnotes.com - articles covering mathematical finance
• Riskglossary.com - online glossary, encyclopedia, and resource locator
• Wilmott.com - The best forum for the quantitative community contributed by from beginners to experts in the field, jobs, articles, training courses etc,
• WilmottWiki Wiki style Quantitative Finance repository
• MoneyScience: News, links and resources in finance and quantitative finance.

[edit] Institutional

• ISDA.org - The International Swaps and Derivatives Association

[edit] Theory

• Prof. Don M. Chance - technical notes covering derivatives and related material
• Prof. Peter Carr (PDF) - FAQs in Option Pricing Theory
• Mathematics of Financial Markets, Prof. Mark Davis, Imperial College
• Option Valuation, Prof. Campbell R. Harvey
• Option Tutor - a visual presentation of modern option pricing theory
• Henk Tijms, Understanding Probability, Chance Rules in Everyday Life, Cambridge University Press, 2003 (Black and Scholes, random walk models, Brownian motion, Kelly's rule)

[edit] Research

• Quantitative Finance Working Papers, global-derivatives.com
• Quantitative Finance Research Papers at the University of Technology, Sydney

[edit] Education

• MS in Financial Mathematics at Middle East Technical University, Ankara, Turkey
• Master's degree in Mathematical Finance at Boston University, Boston, MA, USA.
• MS in Financial Mathematics at the Stanford University, Stanford, CA, USA
• MS in Financial Mathematics at the University of Chicago, Chicago, IL, USA
• MSc in Mathematical Finance at Oxford University, UK
• Master of Quantitative and Computational Finance at Georgia Institute of Technology, GA, USA
• Master of Advanced Studies in Finance at Swiss Federal Institute of Technology Zurich (ETH), Switzerland
• Master of Mathematical Finance at University of Toronto, Toronto, Canada
• Master of Mathematics in Finance at New York University, NY, USA
• Master in Quantitative Economics and Finance at University of St.Gallen (HSG), Switzerland
• MSc in Financial Mathematics at Heriot-Watt, University and the University of Edinburgh
• BA in Financial Mathematics at Asbury College, Wilmore, KY, USA
• BSc Mathematical Finance Specialization at Trent University, Peterborough, ON, Canada

[edit] Training

• Certificate in Quantitative Finance Dr Paul Wilmott et al. at 7city, Live lectures in London and Distant learning via video streaming.
• List of Financial Training Providers: At MoneyScience.

General areas of finance
Financial markets • Investment management • Financial institutions • Personal finance • Public finance • Mathematical finance • Financial economics • Experimental finance • Computational finance