Jump diffusion

From Infogalactic: the planetary knowledge core

Jump to: navigation, search

Jump diffusion is a stochastic process that involves jumps and diffusion. It has important applications in magnetic reconnection, coronal mass ejections, condensed matter physics and in option pricing.

1 In physics
2 In economics and finance
3 See also
4 References

In physics

In crystals, atomic diffusion typically consists of jumps between vacant lattice sites. On time and length scales that average over many single jumps, the net motion of the jumping atoms can be described as regular diffusion.

Jump diffusion can be studied on a microscopic scale by inelastic neutron scattering and by Mößbauer spectroscopy. Closed expressions for the autocorrelation function have been derived for several jump(-diffusion) models:

Singwi, Sjölander 1960:^[1] alternation between oscillatory motion and directed motion
Chudley, Elliott 1961:^[2] jumps on a lattice
Sears 1966,^[3] 1967:^[4] jump diffusion of rotational degrees of freedom
Hall, Ross 1981:^[5] jump diffusion within a restricted volume

In economics and finance

In option pricing, a jump-diffusion model is a form of mixture model, mixing a jump process and a diffusion process. Jump-diffusion models have been introduced by Robert C. Merton as an extension of jump models.^[6] Due to their computational tractability, the special case of a basic affine jump diffusion is popular for some credit risk and short-rate models.^{[citation needed]}

References

↑ Lua error in package.lua at line 80: module 'strict' not found.
↑ Lua error in package.lua at line 80: module 'strict' not found.
↑ Lua error in package.lua at line 80: module 'strict' not found.
↑ Lua error in package.lua at line 80: module 'strict' not found.
↑ Lua error in package.lua at line 80: module 'strict' not found.
↑ Lua error in package.lua at line 80: module 'strict' not found.

Derivatives market

Derivative (finance)

Options

Terms	Credit spread Debit spread Exercise Expiration Moneyness Open interest Pin risk Risk-free interest rate Strike price the Greeks Volatility
Vanilla options	Bond option Call Employee stock option Fixed income FX Option styles Put Warrants
Exotic options	Asian Barrier Basket Binary Chooser Cliquet Commodore Compound Forward start Interest rate Lookback Mountain range Rainbow Swaption
Combinations	Collar Fence Iron butterfly Iron condor Straddle Strangle Covered call Married put Risk reversal
Spreads	Back Bear Box Bull Butterfly Calendar Diagonal Intermarket Ratio Vertical
Valuation	Binomial Black Black–Scholes model Finite difference Garman-Kohlhagen Margrabe's formula Put–call parity Simulation Real options valuation Trinomial Vanna–Volga pricing

Swaps

Exotic derivatives

Other derivatives

Market issues

v t e Volatility
Modelling volatility	Implied volatility Volatility smile Volatility clustering Local volatility Stochastic volatility Jump-diffusion models ARCH and GARCH
Trading volatility	Volatility arbitrage Straddle Volatility swap IVX VIX

v t e Stochastic processes
Discrete time	Bernoulli process Branching process Chinese restaurant process Galton–Watson process Independent and identically distributed random variables Markov chain Moran process Random walk Loop-erased Self-avoiding
Continuous time	Bessel process Birth–death process Brownian motion Bridge Excursion Fractional Geometric Meander Cauchy process Contact process Continuous-time random walk Cox process Diffusion process Empirical process Feller process Fleming–Viot process Gamma process Hunt process Interacting particle systems Itô diffusion Itô process Jump diffusion Jump process Lévy process Local time Markov additive process McKean–Vlasov process Ornstein–Uhlenbeck process Poisson process Compound Non-homogeneous Point process Schramm–Loewner evolution Semimartingale Sigma-martingale Stable process Superprocess Telegraph process Variance gamma process Wiener process Wiener sausage
Both	Branching process Gaussian process Hidden Markov model (HMM) Markov process Martingale Differences Local Sub- Super- Random dynamical system Regenerative process Renewal process White noise
Fields and other	Dirichlet process Gaussian random field Gibbs measure Hopfield model Ising model Potts model Boolean network Markov random field Percolation Pitman–Yor process Point process Cox Poisson Random field Random graph
Time series models	Autoregressive conditional heteroskedasticity (ARCH) model Autoregressive integrated moving average (ARIMA) model Autoregressive (AR) model Autoregressive–moving-average (ARMA) model Generalized autoregressive conditional heteroskedasticity (GARCH) model Moving-average (MA) model
Financial models	Black–Derman–Toy Black–Karasinski Black–Scholes Chen Constant elasticity of variance (CEV) Cox–Ingersoll–Ross (CIR) Garman–Kohlhagen Heath–Jarrow–Morton (HJM) Heston Ho–Lee Hull–White LIBOR market Rendleman–Bartter SABR volatility Vašíček Wilkie
Actuarial models	Bühlmann Cramér–Lundberg Risk process Sparre–Anderson
Queueing models	Bulk Fluid Generalized queueing network M/G/1 M/M/1 M/M/c
Properties	Càdlàg paths Continuous Continuous paths Ergodic Exchangeable Feller-continuous Gauss–Markov Markov Mixing Piecewise deterministic Predictable Progressively measurable Self-similar Stationary Time-reversible
Limit theorems	Central limit theorem Donsker's theorem Doob's martingale convergence theorems Ergodic theorem Fisher–Tippett–Gnedenko theorem Large deviation principle Law of large numbers (weak/strong) Law of the iterated logarithm Maximal ergodic theorem Sanov's theorem
Inequalities	Burkholder–Davis–Gundy Doob's martingale Kunita–Watanabe
Tools	Cameron–Martin formula Convergence of random variables Doléans-Dade exponential Doob decomposition theorem Doob–Meyer decomposition theorem Doob's optional stopping theorem Dynkin's formula Feynman–Kac formula Filtration Girsanov theorem Infinitesimal generator Itô integral Itô's lemma Kolmogorov continuity theorem Kolmogorov extension theorem Lévy–Prokhorov metric Malliavin calculus Martingale representation theorem Optional stopping theorem Prokhorov's theorem Quadratic variation Reflection principle Skorokhod integral Skorokhod's representation theorem Skorokhod space Snell envelope Stochastic differential equation Tanaka Stopping time Stratonovich integral Uniform integrability Usual hypotheses Wiener space Classical Abstract
Disciplines	Actuarial mathematics Econometrics Ergodic theory Extreme value theory (EVT) Large deviations theory Mathematical finance Mathematical statistics Probability theory Queueing theory Renewal theory Ruin theory Statistics Stochastic analysis Time series analysis Machine learning
List of topics Category

This economics-related article is a stub. You can help Wikipedia by expanding it.

This physics-related article is a stub. You can help Wikipedia by expanding it.

This probability-related article is a stub. You can help Wikipedia by expanding it.

Retrieved from "https://infogalactic.com/w/index.php?title=Jump_diffusion&oldid=1076058"

Categories:

Hidden categories:

Jump diffusion

Contents

In physics

In economics and finance

See also

References

Navigation menu

Personal tools

Namespaces

Variants

Views

More

Search

Navigation

Tools