Inference for stochastic volatility models using time change transformations

Καλογερόπουλος, Κωνσταντίνος; Roberts, Gareth O.; Δελλαπόρτας, Πέτρος

doi:10.1214/09-aos702

Cited by 21 publications

(23 citation statements)

References 38 publications

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“…Implementation of the exact-path scheme for Heston’s model is not as simple as in the univariate case, but can be achieved by using simultaneous time-scale transformations t ↦ ϑ V ( t ) and t ↦ ϑ S ( t ) (Kalogeropoulos, Roberts, and Dellaporta, 2010). Even then, the transformations are only possible because the volatility V t itself is a diffusion process:

normald V_{t} = - γ false(V_{t} - μ false) normald t + σ V_{t}^{1 / 2} normald B_{V t}

.…”

Section: Multiresolution Methods In Practicementioning

confidence: 99%

A Multiresolution Method for Parameter Estimation of Diffusion Processes

Kou

Olding²,

Lysy

et al. 2012

Journal of the American Statistical Association

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Diffusion process models are widely used in science, engineering and finance. Most diffusion processes are described by stochastic differential equations in continuous time. In practice, however, data is typically only observed at discrete time points. Except for a few very special cases, no analytic form exists for the likelihood of such discretely observed data. For this reason, parametric inference is often achieved by using discrete-time approximations, with accuracy controlled through the introduction of missing data. We present a new multiresolution Bayesian framework to address the inference difficulty. The methodology relies on the use of multiple approximations and extrapolation, and is significantly faster and more accurate than known strategies based on Gibbs sampling. We apply the multiresolution approach to three data-driven inference problems – one in biophysics and two in finance – one of which features a multivariate diffusion model with an entirely unobserved component.

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normald V_{t} = - γ false(V_{t} - μ false) normald t + σ V_{t}^{1 / 2} normald B_{V t}

.…”

Section: Multiresolution Methods In Practicementioning

confidence: 99%

A Multiresolution Method for Parameter Estimation of Diffusion Processes

Kou

Olding²,

Lysy

et al. 2012

Journal of the American Statistical Association

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“…The integrals above cannot be computed analytically, but the augmented path of v (2000) and Kalogeropoulos et al (2007). In the presence of exact observations the transformations of (13) and (14) …”

Section: Multivariate Stochastic Volatility Modelsmentioning

confidence: 99%

Likelihood-based inference for correlated diffusions

2011

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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.

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“…A very popular class of models which have state-dependent volatility are stochastic volatility models employed in financial econometrics. The methodology of space transformation can be generalised to include time-change methodology to allow models like stochastic volatility models to be addressed, (see Kalogeropoulos et al, 2009). …”

Section: Limitations Of the Methodologymentioning

confidence: 99%

References

2012

Statistical Methods for Stochastic Differential Equations

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This article develops a class of Monte Carlo (MC) methods for simulating conditioned diffusion sample paths, with special emphasis on importance sampling schemes. We restrict attention to a particular type of conditioned diffusions, the so-called diffusion bridge processes. The diffusion bridge is the process obtained by conditioning a diffusion to start and finish at specific values at two consecutive times t 0 < t 1 .Diffusion bridge simulation is a highly non-trivial problem. At an even more elementary level unconditional simulation of diffusions, that is without fixing the value of the process at t 1 , is difficult. This is a simulation from the transition distribution of the diffusion which is typically intractable. This intractability stems from the implicit specification of the diffusion as a solution of a stochastic differential equation (SDE). Although the unconditional simulation can be carried out by various approximate schemes based on discretizations of the SDE, it is not feasible to devise similar schemes for diffusion bridges in general. This has motivated active research in the last 15 years or so for the development of MC methodology for diffusion bridges.

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Inference for stochastic volatility models using time change transformations

Cited by 21 publications

References 38 publications

A Multiresolution Method for Parameter Estimation of Diffusion Processes

A Multiresolution Method for Parameter Estimation of Diffusion Processes

Likelihood-based inference for correlated diffusions

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