What is jump diffusion in finance?
Examples of the jump diffusion model include the Merton model, the Black–Scholes models with jumps, the Kou double exponential jump diffusion model, and several others. This chapter introduces these models by briefly discussing the Poisson process (jumps) and the compound Poisson process. Quantitative Finance.
What is a jump diffusion process?
From Wikipedia, the free encyclopedia. Jump diffusion is a stochastic process that involves jumps and diffusion. It has important applications in magnetic reconnection, coronal mass ejections, condensed matter physics, in Pattern theory and computational vision and in option pricing.
What is a pure jump process?
In this Chapter we consider pure jump processes, that is, processes that change only by jumps. Counting processes and Markov Jump processes are defined and their semimartingale representation is given.
What is Jump process in probability?
A jump process is a type of stochastic process that has discrete movements, called jumps, with random arrival times, rather than continuous movement, typically modelled as a simple or compound Poisson process.
What is Markov jump process?
A Markov jump process is a continuous-time Markov chain if the holding time depends only on the current state. If the holding times of a discrete-time jump process are geometrically distributed, the process is called a Markov jump chain. Thus, such processes have continuous space and continuous time.
What is a Hawkes process?
Hawkes processes are a particularly interesting class of stochastic processes that were introduced in the early seventies by A. G. Hawkes, notably to model the oc- currence of seismic events. Since then they have been applied in diverse areas, from earthquake modeling to financial analysis.
What is a jump chain Markov chain?
The jump chain (Yn) is the discrete time Markov chain on S with initial distribution λ and transition matrix R . The holding times T1,T2,… T 1 , T 2 , … have distribution Tn∼Exp(qYn−1) T n ∼ Exp ( q Y n − 1 ) , and are conditionally independent given (Yn) . The jump times are Jn=T1+T2+⋯+Tn J n = T 1 + T 2 + ⋯ + T n .
Is Hawkes process a Cox process?
The Cox process, named after the British statistician David Cox ( 1955), is a generalisation of the Poisson process. The Hawkes process, named after the British statistician Alan Hawkes ( 1971a, b), is an extension of the Poisson process with self-exciting property, where points show clustering effects.