Numerical Simulation of the Heston Model under Stochastic Correlation
Abstract
:1. Introduction
2. Stochastic Correlation in the Heston Model
3. Path Simulation
3.1. Discretization for the Variance Process
3.2. Discretization for the Correlation Process
3.3. Discretization for the Log Price Process
3.3.1. The Euler and Milstein Scheme (EM Scheme)
3.3.2. The Hybrid Scheme (HB Scheme)
3.4. HB Scheme with Martingale Correction (HBM Scheme)
4. Numerical Results
4.1. A Comparison of the Numerical Methods EM, HB and HBM
4.2. The Effect of Imposing Stochastic Correlation on Implied Volatility
4.3. A Comparison with the Effect of Stochastic Correlation
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
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Case I | Case II | Case III | Case IV | |
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T (maturity) | 10 | 15 | 5 | 10 |
EM | HB | HBM | ||||
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EM | HB | HBM | ||
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EM | HB | HBM | ||
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1 | ||||
1 | ||||
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EM | HB | HBM | ||
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1 | ||||
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1 | ||||
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Teng, L.; Ehrhardt, M.; Günther, M. Numerical Simulation of the Heston Model under Stochastic Correlation. Int. J. Financial Stud. 2018, 6, 3. https://doi.org/10.3390/ijfs6010003
Teng L, Ehrhardt M, Günther M. Numerical Simulation of the Heston Model under Stochastic Correlation. International Journal of Financial Studies. 2018; 6(1):3. https://doi.org/10.3390/ijfs6010003
Chicago/Turabian StyleTeng, Long, Matthias Ehrhardt, and Michael Günther. 2018. "Numerical Simulation of the Heston Model under Stochastic Correlation" International Journal of Financial Studies 6, no. 1: 3. https://doi.org/10.3390/ijfs6010003