Statistical properties and economic implications of jump-diffusion processes with shot-noise effects

Abstract

This paper analyzes the Shot-Noise Jump-Diffusion model of Altmann, Schmidt and Stute (2008), which introduces a new situation where the effects of the arrival of rare, shocking information to the financial markets may fade away in the long run. We analyze several economic implications of the model, providing an analytical expression for the process distribution. We also prove that certain specifications of this model can provide negative serial persistence. Additionally, we find that the degree of serial autocorrelation is related to the arrival and magnitude of abnormal information. Finally, a GMM framework is proposed to estimate the model parameters.

Catastrophe Insurance Modeled by Shot-Noise Processes

“…A possible approach in this direction uses filtering methods and has been started in [30]. The GMM method has been applied to a special class of shot-noise processes in [32]. Further approaches for point process estimation may be found in [33] or [34].…”

Shot-Noise Processes in Finance

“…x 1 `ct with some c ą 0. This case allows for long-memory effects and heavy clustering, compare Moreno et al (2011). In this case, the noise decay is slower than for the exponential case and the effect of the shot persists for longer time in the data.…”

“…Shot-noise processes have been applied to the modelling of stock markets and to the modelling of intensities, which is useful in credit risk and insurance mathematics. Following the works Altmann et al (2008); Schmidt and Stute (2007) and Moreno et al (2011) we consider the application to the modelling of stocks. The main idea is to extend the Black-Scholes-Merton framework by a shot-noise component.…”

“…In the financial and insurance community they have been typically used to efficiently model shock effects, see for example Dassios and Jang (2003), Albrecher and Asmussen (2006), Schmidt and Stute (2007), Altmann et al (2008), Jang et al (2011), Scherer et al (2012, and references therein. Besides this, in Moreno et al (2011) an estimation procedure in a special class of shot-noise processes utilizing the generalized method of moments (GMM) is developed.…”

Equilibruim approach of asset pricing under Lévy process

“…As is known to all, it has been long observed that jumps exist in asset prices. And various stock price processes with jump components have been proposed in the past literature, such as pure jump process by Cox and Ross (1976), jump diffusion process by Merton (1976) and Kou and Wang (2004), and jump diffusion process with short noise by Altmann et al (2008) and Morenno et al (2011). A very general jump diffusion model, which has been commonly used, is Lévy process, since it allows the jump component to have infinite activity and admits nearly an arbitrary distribution.…”