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In mathematical finance, the Black–Derman–Toy model (BDT) is a popular short-rate model used in the pricing of bond options, swaptions and other interest rate derivatives; see Lattice model (finance) § Interest rate derivatives. It is a one-factor model; that is, a single stochastic factor—the short rate—determines the future evolution of all interest rates. It was the first model to com

In mathematics, the Chan–Karolyi–Longstaff–Sanders process (abbreviated as CKLS process) is a stochastic process with applications to finance. In particular it has been used to model the term structure of interest rates. The CKLS process can also be viewed as a generalization of the Ornstein–Uhlenbeck process. It is named after K. C. Chan, G. Andrew Karolyi, Francis A. Longstaff, and Ant

In probability theory, Girsanov's theorem or the Cameron-Martin-Girsanov theorem explains how stochastic processes change under changes in measure.

In probability theory and statistics, a Hawkes process is an age-dependent branching process driven by immigration from an inhomogeneous Poisson process. The process, named after Alan G. Hawkes, is also called a self-exciting point process., i.e., the occurrence of an event increases the likelihood of another event occurring. It has arrivals at times

The Heath–Jarrow–Morton (HJM) framework is a general framework to model the evolution of interest rate curves – instantaneous forward rate curves in particular (as opposed to simple forward rates). When the volatility and drift of the instantaneous forward rate are assumed to be deterministic, this is known as the Gaussian Heath–Jarrow–Morton (HJM) model of forward rates. For direct mode

In finance, the Heston model, named after Steven L. Heston, is a mathematical model that describes the evolution of the volatility of an underlying asset. It is a stochastic volatility model: such a model assumes that the volatility of the asset is not constant, nor even deterministic, but follows a random process.

High frequency data refers to time-series data collected at an extremely fine scale. As a result of advanced computational power in recent decades, high frequency data can be accurately collected at an efficient rate for analysis. Largely used in the financial field, high frequency data provides observations at very frequent intervals that can be used to understand market behaviors, dyna

In financial mathematics, the Hull–White model is a model of future interest rates. In its most generic formulation, it belongs to the class of no-arbitrage models that are able to fit today's term structure of interest rates. It is relatively straightforward to translate the mathematical description of the evolution of future interest rates onto a tree or lattice and so interest rate de

Jump diffusion is a stochastic process that involves jumps and diffusion. It is a type of Lévy process. It has important applications in magnetic reconnection, coronal mass ejections, condensed matter physics, and pattern theory and computational vision.

The Korn–Kreer–Lenssen model (KKL model) is a discrete trinomial model proposed in 1998 by Ralf Korn, Markus Kreer and Mark Lenssen to model illiquid securities and to value financial derivatives on these.

The LIBOR market model, also known as the BGM Model (Brace Gatarek Musiela Model, in reference to the names of some of the inventors) is a financial model of interest rates. It is used for pricing interest rate derivatives, especially exotic derivatives like Bermudan swaptions, ratchet caps and floors, target redemption notes, autocaps, zero coupon swaptions, constant maturity swaps and

In actuarial science and applied probability, ruin theory (sometimes risk theory or collective risk theory) uses mathematical models to describe an insurer's vulnerability to insolvency/ruin. In such models key quantities of interest are the probability of ruin, distribution of surplus immediately prior to ruin, and deficit at time of ruin.

The Snell envelope, used in stochastics and mathematical finance, is the smallest supermartingale dominating a stochastic process. The Snell envelope is named after James Laurie Snell.