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On Weak Predictor-Corrector Schemes for Jump-Diffusion Processes in Finance

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Author Info
Nicola Bruti-Liberati (School of Finance and Economics, University of Technology, Sydney)
Eckhard Platen () (School of Finance and Economics, University of Technology, Sydney)

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Abstract

Event-driven uncertainties such as corporate defaults, operational failures or central bank announcements are important elements in the modelling of financial quantities. Therefore, stochastic differential equations (SDEs) of jump-diffusion type are often used in finance. We consider in this paper weak discrete time approximations of jump-diffusion SDEs which are appropriate for problems such as derivative pricing and the evaluation of risk measures. We present regular and jump-adapted predictor-corrector schemes with first and second order of weak convergence. The regular schemes are constructed on regular time discretizations that do not include jump times, while the jump-adapted schemes are based on time discretizations that include all jump times. A numerical analysis of the accuracy of these schemes when applied to the jump-diffusion Merton model is provided.

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File URL: http://www.business.uts.edu.au/qfrc/research/research_papers/rp179.pdf
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Publisher Info
Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 179.

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Length: 15
Date of creation: 01 Jul 2006
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Handle: RePEc:uts:rpaper:179

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Related research
Keywords: weak approximations; Monte Carlo simulations; predictor-corrector schemes; jump diffusions;

Find related papers by JEL classification:
G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
C63 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computational Techniques

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Mark Joshi & Alan Stacey, 2008. "New and robust drift approximations for the LIBOR market model," Quantitative Finance, Taylor and Francis Journals, vol. 8(4), pages 427-434. [Downloadable!] (restricted)
  2. Nicola Bruti-Liberati & Eckhard Platen, 2005. "On the Strong Approximation of Jump-Diffusion Processes," Research Paper Series 157, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  3. Michael Johannes, 2004. "The Statistical and Economic Role of Jumps in Continuous-Time Interest Rate Models," Journal of Finance, American Finance Association, vol. 59(1), pages 227-260, 02. [Downloadable!] (restricted)
  4. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 9(1), pages 69-107. [Downloadable!] (restricted)
  5. Philippe Jorion, 1988. "On Jump Processes in the Foreign Exchange and Stock Markets," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 1(4), pages 427-445. [Downloadable!] (restricted)
  6. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144. [Downloadable!] (restricted)
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  7. Nicola Bruti Liberati & Eckhard Platen, 2004. "On the Efficiency of Simplified Weak Taylor Schemes for Monte Carlo Simulation in Finance," Research Paper Series 114, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  8. Paul Glasserman & S. G. Kou, 2003. "The Term Structure of Simple Forward Rates with Jump Risk," Mathematical Finance, Blackwell Publishing, vol. 13(3), pages 383-410. [Downloadable!] (restricted)
  9. Kestutis Kubilius & Eckhard Platen, 2001. "Rate of Weak Convergence of the Euler Approximation for Diffusion Processes with Jumps," Research Paper Series 54, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
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