Financial mathematics

Financial mathematics is the branch of applied mathematics concerned with the financial markets. The subject naturally has a close relationship with the discipline of financial economics, however the subject is narrower in scope and more abstract. A central difference is that whilst a financial economist might study the structural reasons why a company may have a certain share price, a 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.

Financial mathematics articles

Mathematical tools

• Probability
• Probability distribution
  • Binomial distribution
  • Log-normal distribution
• Expected value
• Value at risk
• Risk-neutral measure
• Stochastic calculus
• Brownian motion
• Itô's lemma
• 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
• Mathematical model
• Numerical method

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 formula
    • Black model
    • Binomial options model
    • Implied volatility
      • Volatility smile
    • The Greeks
• Interest rate derivatives
  • Short rate model
    • Hull-White model
  • Brace-Gatarek-Musiela model
  • Heath-Jarrow-Morton framework

Compare

• Mathematical economics
• Extreme value theory

See also

• Financial Engineering
• Derivative securities, list of derivatives topics
• Fundamental financial concepts – topics
• Model (economics)

Related articles

• 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

External links

• ISDA.org – The International Swaps and Derivatives Association
• Quantitative Mathematics Glossary – a guide to derivatives and risk terminology from Global-Derivatives
• Quantnotes.com – introductory articles covering mathematical finance
• technical notes covering derivatives and related material, Prof. Don M. Chance
• rmetrics.org – A R based environment for teaching financial engineering and computational finance
• finmath.com – Financial Mathematics Reading List
• Moneyscience.org – An open-access resource for academics and practitioners working in finance and economics, physics, applied mathematics and computing.
• Riskglossary.com – an online glossary, encyclopedia, and resource locator
• Option Tutor – a visual presentation of modern option pricing theory
• Riskworx.com – discussion of the application and theory of derivatives
• QuantFinanceJobs.com – specialist job board for financial engineers