Big Data and Information Analytics

2018, Issue 2:24-40. doi: 10.3934/bdia.2018005
Research article

Estimating option prices using multilevel particle filters

• Received: 14 October 2018 Accepted: 30 October 2018 Published: 20 November 2018
• Option valuation problems are often solved using standard Monte Carlo (MC) methods. These techniques can often be enhanced using several strategies especially when one discretizes the dynamics of the underlying asset, of which we assume follows a diffusion process. We consider the combination of two methodologies in this direction. The first is the well-known multilevel Monte Carlo (MLMC) method [7], which is known to reduce the computational effort to achieve a given level of mean square error (MSE) relative to MC in some cases. Sequential Monte Carlo (SMC) (or the particle filter (PF)) methods (e.g. [6]) have also been shown to be beneficial in many option pricing problems potentially reducing variances by large magnitudes (relative to MC) [11, 17]. We propose a multilevel particle filter (MLPF) as an alternative approach to price options. We show via numerical simulations that under suitable assumptions regarding the discretization of the SDE driven by Brownian motion the cost to obtain O$(\epsilon^2)$ MSE scales like O$(\epsilon^{-2.5})$ for our method, as compared with the standard particle filter O$(\epsilon^{-3})$.

Citation: Prince Peprah Osei, Ajay Jasra. Estimating option prices using multilevel particle filters[J]. Big Data and Information Analytics, 2018, 3(2): 24-40. doi: 10.3934/bdia.2018005

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• Option valuation problems are often solved using standard Monte Carlo (MC) methods. These techniques can often be enhanced using several strategies especially when one discretizes the dynamics of the underlying asset, of which we assume follows a diffusion process. We consider the combination of two methodologies in this direction. The first is the well-known multilevel Monte Carlo (MLMC) method [7], which is known to reduce the computational effort to achieve a given level of mean square error (MSE) relative to MC in some cases. Sequential Monte Carlo (SMC) (or the particle filter (PF)) methods (e.g. [6]) have also been shown to be beneficial in many option pricing problems potentially reducing variances by large magnitudes (relative to MC) [11, 17]. We propose a multilevel particle filter (MLPF) as an alternative approach to price options. We show via numerical simulations that under suitable assumptions regarding the discretization of the SDE driven by Brownian motion the cost to obtain O$(\epsilon^2)$ MSE scales like O$(\epsilon^{-2.5})$ for our method, as compared with the standard particle filter O$(\epsilon^{-3})$.

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沈阳化工大学材料科学与工程学院 沈阳 110142

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