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Likelihood-based inference for correlated diffusions

Author

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  • Konstantinos Kalogeropoulos
  • Petros Dellaportas
  • Gareth O. Roberts

Abstract

We address the problem of likelihood based inference for correlated diffusion processes using Markov chain Monte Carlo (MCMC) techniques. Such a task presents two interesting problems. First, the construction of the MCMC scheme should ensure that the correlation coefficients are updated subject to the positive definite constraints of the diffusion matrix. Second, a diffusion may only be observed at a finite set of points and the marginal likelihood for the parameters based on these observations is generally not available. We overcome the first issue by using the Cholesky factorisation on the diffusion matrix. To deal with the likelihood unavailability, we generalise the data augmentation framework of Roberts and Stramer (2001 Biometrika 88(3):603-621) to d-dimensional correlated diffusions including multivariate stochastic volatility models. Our methodology is illustrated through simulation based experiments and with daily EUR /USD, GBP/USD rates together with their implied volatilities.

Suggested Citation

  • Konstantinos Kalogeropoulos & Petros Dellaportas & Gareth O. Roberts, 2007. "Likelihood-based inference for correlated diffusions," Papers 0711.1595, arXiv.org.
    • Handle: RePEc:arx:papers:0711.1595
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    References listed on IDEAS

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    1. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," The Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
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    3. Kalogeropoulos, Konstantinos, 2007. "Likelihood-based inference for a class of multivariate diffusions with unobserved paths," LSE Research Online Documents on Economics 31423, London School of Economics and Political Science, LSE Library.
    4. Kalogeropoulos, Konstantinos & Roberts, Gareth O. & Dellaportas, Petros, 2007. "Inference for stochastic volatility model using time change transformations," MPRA Paper 5697, University Library of Munich, Germany.
    5. Alexandros Beskos & Omiros Papaspiliopoulos & Gareth O. Roberts & Paul Fearnhead, 2006. "Exact and computationally efficient likelihood‐based estimation for discretely observed diffusion processes (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 333-382, June.
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    Cited by:

    1. Beskos, Alexandros & Kalogeropoulos, Konstantinos & Pazos, Erik, 2013. "Advanced MCMC methods for sampling on diffusion pathspace," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1415-1453.
    2. Paolo Giudici & Laura Parisi, 2015. "Modeling Systemic Risk with Correlated Stochastic Processes," DEM Working Papers Series 110, University of Pavia, Department of Economics and Management.
    3. Kalogeropoulos, Konstantinos & Roberts, Gareth O. & Dellaportas, Petros, 2007. "Inference for stochastic volatility model using time change transformations," MPRA Paper 5697, University Library of Munich, Germany.
    4. Paolo Giudici & Laura Parisi, 2016. "CoRisk: measuring systemic risk through default probability contagion," DEM Working Papers Series 116, University of Pavia, Department of Economics and Management.
    5. Paolo Giudici & Laura Parisi, 2017. "Sovereign risk in the Euro area: a multivariate stochastic process approach," Quantitative Finance, Taylor & Francis Journals, vol. 17(12), pages 1995-2008, December.

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    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General

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