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.
Girsanov's theoremStochastic processes Theorems In probability theory, Girsanov's theorem tells how stochastic processes change under changes in measure. The theorem is especially important in the theory of financial mathematics as it tells how to convert from the physical
Monte Carlo methodMonte Carlo methods are algorithms for solving various kinds of computational problems by using random numbers (or more often pseudo-random numbers), as opposed to deterministic algorithms. Monte Carlo methods are extremely important in computational phys
Partial differential equationIn mathematics, and in particular calculus, a partial differential equation PDE is an equation involving partial derivatives of an unknown function. The idea is to describe a function indirectly by a relation between itself and its partial derivatives, ras
Heat equationThe heat equation or diffusion equation is an important partial differential equation which describes the variation of temperature in a given region over time. In the special case of a heat propagation in an isotropic and homogeneous medium, this equation
VolatilityVolatility is the standard deviation of the change in value of a financial instrument with a specific time horizon. It is often used to quantify the risk of the instrument over that time period. Volatility is typically expressed in annualized terms, and i
ARCH modelIn econometrics, an autoregressive conditional heteroskedasticity (ARCH) model considers the variance of the current error term to be a function of the variances of the previous time periods' error terms. If an autoregressive moving average model is assum
