Topic
Jump diffusion
About: Jump diffusion is a research topic. Over the lifetime, 2422 publications have been published within this topic receiving 42251 citations.
Papers published on a yearly basis
Papers
30 Dec 2003
TL;DR: In this article, the authors provide a self-contained overview of the theoretical, numerical, and empirical aspects involved in using jump processes in financial modelling, and it does so in terms within the grasp of nonspecialists.
Abstract: WINNER of a Riskbook.com Best of 2004 Book Award!During the last decade, financial models based on jump processes have acquired increasing popularity in risk management and option pricing. Much has been published on the subject, but the technical nature of most papers makes them difficult for nonspecialists to understand, and the mathematical tools required for applications can be intimidating. Potential users often get the impression that jump and Levy processes are beyond their reach.Financial Modelling with Jump Processes shows that this is not so. It provides a self-contained overview of the theoretical, numerical, and empirical aspects involved in using jump processes in financial modelling, and it does so in terms within the grasp of nonspecialists. The introduction of new mathematical tools is motivated by their use in the modelling process, and precise mathematical statements of results are accompanied by intuitive explanations.Topics covered in this book include: jump-diffusion models, Levy processes, stochastic calculus for jump processes, pricing and hedging in incomplete markets, implied volatility smiles, time-inhomogeneous jump processes and stochastic volatility models with jumps. The authors illustrate the mathematical concepts with many numerical and empirical examples and provide the details of numerical implementation of pricing and calibration algorithms.This book demonstrates that the concepts and tools necessary for understanding and implementing models with jumps can be more intuitive that those involved in the Black Scholes and diffusion models. If you have even a basic familiarity with quantitative methods in finance, Financial Modelling with Jump Processes will give you a valuable new set of tools for modelling market fluctuations.
3,935 citations
TL;DR: In this article, a double exponential jump-diffusion model is proposed for option pricing, which is simple enough to produce analytical solutions for a variety of option-pricing problems, including call and put options, interest rate derivatives, and path dependent options.
Abstract: Brownian motion and normal distribution have been widely used in the Black--Scholes option-pricing framework to model the return of assets. However, two puzzles emerge from many empirical investigations: the leptokurtic feature that the return distribution of assets may have a higher peak and two (asymmetric) heavier tails than those of the normal distribution, and an empirical phenomenon called "volatility smile" in option markets. To incorporate both of them and to strike a balance between reality and tractability, this paper proposes, for the purpose of option pricing, a double exponential jump-diffusion model. In particular, the model is simple enough to produce analytical solutions for a variety of option-pricing problems, including call and put options, interest rate derivatives, and path-dependent options. Equilibrium analysis and a psychological interpretation of the model are also presented.
1,839 citations
TL;DR: In this article, the authors examined the empirical performance of jump diffusion models of stock price dynamics from joint options and stock markets data and found that these models fare better in fitting options and returns data simultaneously.
Abstract: This paper examines the empirical performance of jump diffusion models of stock price dynamics from joint options and stock markets data. The paper introduces a model with discontinuous correlated jumps in stock prices and stock price volatility, and with state-dependent arrival intensity. We discuss how to perform likelihoodbased inference based upon joint options/returns data and present estimates of risk premiums for jump and volatility risks. The paper finds that while complex jump specifications add little explanatory power in fitting options data, these models fare better in fitting options and returns data simultaneously. THE STATISTICAL PROPERTIES of stock returns have long been of interest to finan
1,351 citations
TL;DR: In this article, the role of various volatility specifications, such as multiple stochastic volatility (SV) factors and jump components, in appropriate modeling of equity return distributions is evaluated.
1,107 citations
1 Feb 1961
TL;DR: In this article, the incoherent inelastic scattering cross section of slow neutrons from liquids is calculated using a simple model in which the liquid is assumed to have appreciable short range order in a quasi-crystalline form.
Abstract: The incoherent inelastic scattering cross section of slow neutrons from liquids is calculated using a simple model in which the liquid is assumed to have appreciable short range order in a quasi-crystalline form. Diffusive motion takes place in large discrete jumps, between which the atoms oscillate as in a solid. The model predicts a definite, easily calculable cross section which is not dominated by diffusion effects as when continuous diffusion is assumed, but shows a characteristic variation with angle which could be looked for experimentally. The related pair correlation functions are dominated at small r and t by vibrational effects. Although simple and extreme the model explains several aspects of the observations of Brockhouse and Pope in 1959 and others. A brief discussion of the coherent scattering cross sections for the model is given although explicit formulae are not obtained.
712 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 60 |
| 2024 | 71 |
| 2023 | 99 |
| 2022 | 170 |
| 2021 | 152 |
| 2020 | 124 |