Optimal Filtering of Jump Diffusions: Extracting Latent States from Asset Prices

Johannes, Michael; Polson, Nicholas G.; Stroud, Jonathan

doi:10.1093/rfs/hhn110

Cited by 176 publications

(115 citation statements)

References 72 publications

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“…Filtering for both parameters and state has been discussed by Liu and West (2001), Stroud et al (2004) and Johannes et al (2006). We consider data …”

Section: Sequential Filtering For Parameters and State -The Simulatiomentioning

confidence: 99%

Bayesian inference for nonlinear multivariate diffusion models observed with error

Golightly

Wilkinson

2008

Computational Statistics & Data Analysis

181

183

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Diffusion processes governed by stochastic differential equations (SDEs) are a well established tool for modelling continuous time data from a wide range of areas. Consequently, techniques have been developed to estimate diffusion parameters from partial and discrete observations. Likelihood based inference can be problematic as closed form transition densities are rarely available. One widely used solution involves the introduction of latent data points between every pair of observations to allow an Euler-Maruyama approximation of the true transition densities to become accurate. In recent literature, Markov chain Monte Carlo (MCMC) methods have been used to sample the posterior distribution of latent data and model parameters; however, naive schemes suffer from a mixing problem that worsens with the degree of augmentation. In this paper, we explore an MCMC scheme whose performance is not adversely affected by the number of latent values. We illustrate the methodology by estimating parameters governing an auto-regulatory gene network, using partial and discrete data that is subject to measurement error.

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“…Filtering for both parameters and state has been discussed by Liu and West (2001), Stroud et al (2004) and Johannes et al (2006). We consider data …”

Section: Sequential Filtering For Parameters and State -The Simulatiomentioning

confidence: 99%

Bayesian inference for nonlinear multivariate diffusion models observed with error

Golightly

Wilkinson

2008

Computational Statistics & Data Analysis

181

183

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“…2 Time-consistent estimation methods have been previously used to calibrate models to index returns and options. See, e.g., Pan (2002), Eraker (2004), Broadie et al (2007), Christoffersen et al (2010), Johannes et al (2009) and Duan and Yeh (2011). However, as underlined in Ferriani and Pastorello (2012), most papers filtering information from option prices rely on one option per day or a limited set of options.…”

Section: Introductionmentioning

confidence: 99%

Inferring Volatility Dynamics and Risk Premia from the S&P 500 and VIX Markets

2016

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This paper studies the information content of the S&P 500 and VIX markets on the volatility of the S&P 500 returns. We estimate a flexible affine model based on a joint time series of underlying indexes and option prices on both markets. An extensive model specification analysis reveals that jumps and a stochastic level of reversion for the variance help reproduce risk-neutral distributions as well as the term structure of volatility smiles and of variance risk premia. We find that the S&P 500 and VIX derivatives prices are consistent in times of market calm but contain conflicting information on the variance during market distress.

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“…The calculation of total likelihood (equation (7)) proceeds incrementally as the state and volatility are advanced from time t i−1 to t i using recursive particle filtering [5,7].…”

Section: Recursive Filteringmentioning

confidence: 99%

A Heterogeneous Computing Approach to Simulation of the Heston Stochastic Volatility Model

Hurn

Lindsay

Warne

2016

ANZIAMJ

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Stochastic volatility models are of fundamental importance to the pricing of derivatives. One of the most commonly used models of stochastic volatility is the Heston model in which the price and volatility of an asset evolve as a pair of coupled stochastic differential equations. The computation of asset prices and volatilities involves the simulation of many sample trajectories with conditioning. The problem is treated using the method of particle filtering. While the simulation of a shower of particles is computationally expensive, each particle behaves independently making such simulations ideal for massively parallel heterogeneous computing platforms. We present a portable Opencl implementation of the Heston model and discuss its performance and

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Optimal Filtering of Jump Diffusions: Extracting Latent States from Asset Prices

Cited by 176 publications

References 72 publications

Bayesian inference for nonlinear multivariate diffusion models observed with error

Bayesian inference for nonlinear multivariate diffusion models observed with error

Inferring Volatility Dynamics and Risk Premia from the S&P 500 and VIX Markets

A Heterogeneous Computing Approach to Simulation of the Heston Stochastic Volatility Model

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