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Covariate-based stochastic parameterization of baroclinic ocean eddies

100%

Verheul N., Viebahn J., Crommelin D.

Mathematics of Climate and Weather Forecasting

2017

tom 3

nr 1

90-117

In this study we investigate a covariate-based stochastic approach to parameterize unresolved turbulent processes within a standard model of the idealised, wind-driven ocean circulation. We focus on vertical instead of horizontal coarse-graining, such that we avoid the subtle difficulties of horizontal coarsegraining. The corresponding eddy forcing is uniquely defined and has a clear physical interpretation related to baroclinic instability.We propose to emulate the baroclinic eddy forcing by sampling from the conditional probability distribution functions of the eddy forcing obtained from the baroclinic reference model data. These conditional probability distribution functions are approximated here by sampling uniformly from discrete reference values. We analyze in detail the different performances of the stochastic parameterization dependent on whether the eddy forcing is conditioned on a suitable flow-dependent covariate or on a timelagged covariate or on both. The results demonstrate that our non-Gaussian, non-linear methodology is able to accurately reproduce the first four statistical moments and spatial/temporal correlations of the stream function, energetics, and enstrophy of the reference baroclinic model.

Calibration and simulation of Heston model

100%

Mrázek M., Pospíšil J.

Open Mathematics

2017

tom 15

nr 1

679-704

We calibrate Heston stochastic volatility model to real market data using several optimization techniques. We compare both global and local optimizers for different weights showing remarkable differences even for data (DAX options) from two consecutive days. We provide a novel calibration procedure that incorporates the usage of approximation formula and outperforms significantly other existing calibration methods. We test and compare several simulation schemes using the parameters obtained by calibration to real market data. Next to the known schemes (log-Euler, Milstein, QE, Exact scheme, IJK) we introduce also a new method combining the Exact approach and Milstein (E+M) scheme. Test is carried out by pricing European call options by Monte Carlo method. Presented comparisons give an empirical evidence and recommendations what methods should and should not be used and why. We further improve the QE scheme by adapting the antithetic variates technique for variance reduction.

Ograniczanie wyników

1 Mathematics of Climate and Weather Forecasting

1 Open Mathematics

1 Crommelin D.

1 Mrázek M.

1 Pospíšil J.

1 Verheul N.

1 Viebahn J.

2 2017

Wyniki wyszukiwania

Covariate-based stochastic parameterization of baroclinic ocean eddies

Calibration and simulation of Heston model