# Quasi-Monte Carlo methods for the Heston model

@inproceedings{Baldeaux2012QuasiMonteCM, title={Quasi-Monte Carlo methods for the Heston model}, author={Jan Baldeaux and Dale O. Roberts}, year={2012} }

In this paper, we discuss the application of quasi-Monte Carlo methods to the Heston model. We base our algorithms on the Broadie-Kaya algorithm, an exact simulation scheme for the Heston model. As the joint transition densities are not available in closed-form, the Linear Transformation method due to Imai and Tan, a popular and widely applicable method to improve the effectiveness of quasi-Monte Carlo methods, cannot be employed in the context of path-dependent options when the underlying…

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## References

SHOWING 1-10 OF 54 REFERENCES

Quasi-Monte Carlo for finance beyond Black-Scholes

- Mathematics
- 2009

Quasi-Monte Carlo methods are used to approximate integrals of high dimensionality. However, if the problem under consideration is of unbounded dimensionality, it is not obvious if one can apply…

A QUASI-MONTE CARLO ALGORITHM FOR THE NORMAL INVERSE GAUSSIAN DISTRIBUTION AND VALUATION OF FINANCIAL DERIVATIVES

- Mathematics
- 2006

We propose a quasi-Monte Carlo (qMC) algorithm to simulate variates from the normal inverse Gaussian (NIG) distribution. The algorithm is based on a Monte Carlo technique found in Rydberg [13], and…

Efficient Monte Carlo and Quasi - Monte Carlo Option Pricing Under the Variance Gamma Model

- Mathematics, Computer ScienceManag. Sci.
- 2006

This work develops and study efficient Monte Carlo algorithms for pricing path-dependent options with the variance gamma model, and combines the gamma bridge sampling with randomized quasi--Monte Carlo to reduce the variance and thus further improve the efficiency.

Quasi-Monte Carlo methods for the Kou model

- Computer Science, MathematicsMonte Carlo Methods Appl.
- 2008

QMC approaches are introduced for the integration problems pertaining to the Poisson processes, compoundPoisson processes and jump-diffusion processes underlying the Kou model as opposed to increment-by-increment approaches.

An Accelerating Quasi-Monte Carlo Method for Option Pricing Under the Generalized Hyperbolic L[e-acute]vy Process

- Mathematics, Computer ScienceSIAM J. Sci. Comput.
- 2009

This paper develops a simple and yet practically efficient algorithm for simulating high-dimensional exotic options based on an extension of Imai and Tan's linear transformation method that can be used to enhance quasi-Monte Carlo method in a wide range of applications.

Monte Carlo Methods and Models in Finance and Insurance

- Economics
- 2010

Introduction and User Guide Introduction and concept Contents How to use this book? Further literature Acknowledgements Generating Random Numbers Introduction Examples of random number generators…

Quasi-Monte Carlo Methods in Financial Engineering: An Equivalence Principle and Dimension Reduction

- Mathematics, Computer ScienceOper. Res.
- 2011

Whereas in QMC all the common methods may lose their power in some situations, the new method behaves very well in all cases, and can be interpreted as a practical way of reducing the effective dimension for some class of functions.

Stratified sampling and quasi-Monte Carlo simulation of Lévy processes

- Mathematics, Computer ScienceMonte Carlo Methods Appl.
- 2006

We provide a method for the generation of paths of Lévy processes which allows for more efficient simulation than crude step-by-step generation. We show how, using our method, one can apply…

Exact simulation of option Greeks under stochastic volatility and jump diffusion models

- Computer Science, MathematicsProceedings of the 2004 Winter Simulation Conference, 2004.
- 2004

Monte Carlo simulation estimators are derived to compute Greeks under Heston's stochastic volatility model and some variants of it which include jumps in the price and variance processes to generate unbiased estimates of option price derivatives in these models.

Specification Analysis of Affine Term Structure Models

- Mathematics, Economics
- 1997

In this paper, we explore the features of affine term structure models that are empirically important for explaining the joint distribution of yields on short and long-term interest rate swaps. We…