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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.

Dependent defaults and losses with factor copula models

81%

Ackerer D., Vatter T.

Dependence Modeling

2017

tom 5

nr 1

375-399

We present a class of flexible and tractable static factor models for the term structure of joint default probabilities, the factor copula models. These high-dimensional models remain parsimonious with paircopula constructions, and nest many standard models as special cases. The loss distribution of a portfolio of contingent claims can be exactly and efficiently computed when individual losses are discretely supported on a finite grid. Numerical examples study the key features affecting the loss distribution and multi-name credit derivatives prices. An empirical exercise illustrates the flexibility of our approach by fitting credit index tranche prices.

Ograniczanie wyników

1 Dependence Modeling

1 Open Mathematics

1 Ackerer D.

1 Mrázek M.

1 Pospíšil J.

1 Vatter T.

2 2017

Wyniki wyszukiwania

Calibration and simulation of Heston model

Dependent defaults and losses with factor copula models