Abstract
Particle Filter algorithms for filtering latent states (volatility and jumps) of Stochastic-Volatility Jump-Diffusion (SVJD) models are being explained. Three versions of the SIR particle filter with adapted proposal distributions to the jump occurrences, jump sizes, and both are derived and their performance is compared in a simulation study to the un-adapted particle filter. The filter adapted to both the jump occurrences and jump sizes achieves the best performance, followed in their respective order by the filter adapted only to the jump occurrences and the filter adapted only to the jump sizes. All adapted particle filters outperformed the unadapted particle filter.
Highlights
Modelling of volatility and jumps in financial time series plays an important role in many areas of finance, such as asset pricing, portfolio optimisation, VaR estimation, option valuation or quantitative trading
To cope with this problem, we derive three possible adaptation schemes, adapting the SIR particle filter either to the jump occurrences, jump sizes, or both, and we show in a simulation study that these jump-adapted particle filters dramatically outperform the un-adapted particle filter
As the proposal density of the un-adapted particle filter does not utilise the information about the observation yt, it is suboptimal and it tends to propose many latent state values that end up being discarded during the weight update and re-sampling step
Summary
Modelling of volatility and jumps in financial time series plays an important role in many areas of finance, such as asset pricing, portfolio optimisation, VaR estimation, option valuation or quantitative trading. While the un-adapted SIR particle filter (Gordon et al 1993) represents a universal filtering approach, its sampling efficiency may be low (Pitt and Shephard, 1999), which turns out to be problematic when it is applied for the filtering of SVJD model jumps, especially if they are rare. To cope with this problem, we derive three possible adaptation schemes, adapting the SIR particle filter either to the jump occurrences, jump sizes, or both, and we show in a simulation study that these jump-adapted particle filters dramatically outperform the un-adapted particle filter. We conclude the results and discuss possible areas for future research
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