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

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