Mathematical finance
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(Redirected from Financial mathematics)
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 (see: Valuation of options).
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-free pricing is one of the key theorems in mathematical finance.
Many universities around the world now offer degree and research programs in mathematical finance.
Mathematical finance articles
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
- Martingale representation theorem
- Feynman Kac Formula
- Stochastic differential equations
- Volatility
- Stochastic volatility
- Mathematical model
- Numerical method
- Numerical partial differential equations
- Crank-Nicolson method
- Finite difference method
Derivatives pricing
- Rational pricing assumptions
- Risk neutral valuation
- Arbitrage-free pricing
- Futures
- 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