Mathematical finance

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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 field of computational finance (also known as financial engineering). Arguably, these are largely synonymous, although the latter focuses on application, while the former focuses on modeling and derivation; see Quantitative analyst.

The fundamental theorem of arbitrage pricing is one of the key theorems in mathematical finance.

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

[edit] Mathematical finance articles

[edit] Mathematical tools

• Calculus
• Differential equation
• 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
• 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)
  • Intrinsic value, Time value
  • Moneyness
  • Pricing models
    • Black–Scholes model
    • Black model
    • Binomial options model
    • Monte Carlo option model
    • Implied volatility, Volatility smile
    • SABR Volatility Model
    • The Greeks
  • Optimal stopping (Pricing of American options)
• Interest rate derivatives
  • Short rate model
    • Hull-White model
    • Cox-Ingersoll-Ross model
    • Chen model
  • LIBOR Market Model
  • Heath-Jarrow-Morton framework

[edit] See also

• Computational finance
• Quantitative Behavioral Finance
• Derivative (finance), list of derivatives topics
• Modeling and analysis of financial markets
• International Swaps and Derivatives Association
• Fundamental financial concepts - topics
• Model (economics)
• List of finance topics
• List of economics topics, List of economists
• List of accounting topics
• List of marketing topics
• List of management topics

[edit] External links

• Global Derivatives Quantitative Mathematics Glossary
• Mathematics of Financial Markets, Prof. Mark Davis, Imperial College
• Option Valuation, Prof. Campbell R. Harvey
• Oxford-Man Institute, University of Oxford
• Quantitative Finance Research Papers at the University of Technology, Sydney

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