An almost exact simulation method for the Heston model

2007 ◽  
Vol 11 (1) ◽  
pp. 115-125 ◽  
Author(s):  
Robert Smith
Keyword(s):  
Simulation Method ◽  
Heston Model ◽  
Exact Simulation

scholarly journals Key Technique of Almost Exact Simulation for Non-affine Heston Model

2020 ◽  
Vol 1624 ◽  
pp. 022016
Author(s):  
Xingyin Liang ◽  
Youfa Sun ◽  
Yuhang Yao
Keyword(s):  
Heston Model ◽  
Exact Simulation

scholarly journals Dimensioning of Fairway Bends—Kinematic Method of Numerical Simulation

2020 ◽  
Vol 8 (2) ◽  
pp. 138
Author(s):  
Stanisław Gucma ◽  
Marcin Przywarty ◽  
Jan Dzwonkowski ◽  
Mateusz Bilewski
Keyword(s):  
Numerical Simulation ◽  
Numerical Simulations ◽  
Simulation Method ◽  
High Accuracy ◽  
Concept Design ◽  
Exact Simulation ◽  
Centre Of Gravity ◽  
Kinematic Method ◽  
Low Costs ◽  
Simulation Results

The article presents a new kinematic method of numerical simulation intended for establishing dimensions of safe manoeuvring areas of bends in various types of fairways for vessels of specific parameters. The method consists of multiple numerical simulations of a ship’s passage (ship’s centre of gravity) through a bend, representing the entire physically possible movement of the ship, and an analysis of simulation results. The developed method was verified on the bends of the Świnoujście–Szczecin fairway, by comparing the results to the exact simulation method of a ship’s movements. The relatively high accuracy and low costs of the method allow it to be used in a concept design of built or modern waterway systems.

scholarly journals Exact Simulation for Diffusion Bridges: An Adaptive Approach

2014 ◽  
Vol 51 (02) ◽  
pp. 346-358
Author(s):  
Hongsheng Dai
Keyword(s):  
Brownian Motion ◽  
Sampling Methods ◽  
Simulation Method ◽  
New Method ◽  
Sampling Techniques ◽  
Rejection Sampling ◽  
Exact Simulation ◽  
Adaptive Approach

Exact simulation approaches for a class of diffusion bridges have recently been proposed based on rejection sampling techniques. The existing rejection sampling methods may not be practical owing to small acceptance probabilities. In this paper we propose an adaptive approach that improves the existing methods significantly under certain scenarios. The idea of the new method is based on a layered process, which can be simulated from a layered Brownian motion with reweighted layer probabilities. We will show that the new exact simulation method is more efficient than existing methods theoretically and via simulation.

scholarly journals EFFICIENT, ALMOST EXACT SIMULATION OF THE HESTON STOCHASTIC VOLATILITY MODEL

2010 ◽  
Vol 13 (01) ◽  
pp. 1-43 ◽  
Author(s):  
ALEXANDER VAN HAASTRECHT ◽  
ANTOON PELSSER
Keyword(s):  
Stochastic Volatility ◽  
Numerical Study ◽  
Three Dimensional ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Simulation Methods ◽  
Exact Simulation ◽  
Volatility Model ◽  
Chi Squared ◽  
Chi Squared Distribution

We deal with discretization schemes for the simulation of the Heston stochastic volatility model. These simulation methods yield a popular and flexible pricing alternative for pricing and managing a book of exotic derivatives which cannot be valued using closed-form expressions. For the Heston dynamics an exact simulation method was developed by Broadie and Kaya (2006), however we argue why its practical use is limited. Instead we focus on efficient approximations of the exact scheme, aimed to resolve the disadvantages of this method; one of the main bottlenecks in the exact scheme is the simulation of the Non-central Chi-squared distributed variance process, for which we suggest an efficient caching technique. At first sight the creation of a cache containing the inverses of this distribution might seem straightforward, however as the parameter space of the inverse Non-central Chi-squared distribution is three-dimensional, the design of such a direct cache is rather complicated, as pointed out by Broadie and Andersen. Nonetheless, for the case of the Heston model we are able to tackle this dimensionality problem and show that the three-dimensional inverse of the non-central chi-squared distribution can effectively be reduced to a one dimensional cache. The performed analysis hence leads to the development of three new efficient simulation methods (the NCI, NCI-QE and BK-DI scheme). Finally, we conclude with a comprehensive numerical study of these new schemes and the exact scheme of Broadie and Kaya, the almost exact scheme of Smith, the Kahl-Jäckel scheme, the FT scheme of Lord et al. and the QE-M scheme of Andersen. From these results, we find that the QE-M scheme is the most efficient, followed closely by the NCI-M, NCI-QE-M and BK-DI-M schemes, whilst we observe that all other considered schemes perform a factor 6 to 70 times less efficient than the latter four methods.

scholarly journals Exact simulation of multidimensional reflected Brownian motion

2018 ◽  
Vol 55 (1) ◽  
pp. 137-156
Author(s):  
Jose Blanchet ◽  
Karthyek Murthy
Keyword(s):  
Brownian Motion ◽  
Information Structure ◽  
Piecewise Linear ◽  
Simulation Method ◽  
Uniform Norm ◽  
Piecewise Linear Approximation ◽  
Reflected Brownian Motion ◽  
Proposal Distribution ◽  
Exact Simulation ◽  
Simulation Techniques

AbstractWe present the first exact simulation method for multidimensional reflected Brownian motion (RBM). Exact simulation in this setting is challenging because of the presence of correlated local-time-like terms in the definition of RBM. We apply recently developed so-called ε-strong simulation techniques (also known as tolerance-enforced simulation) which allow us to provide a piecewise linear approximation to RBM with ε (deterministic) error in uniform norm. A novel conditional acceptance–rejection step is then used to eliminate the error. In particular, we condition on a suitably designed information structure so that a feasible proposal distribution can be applied.

Sign in / Sign up

Export Citation Format

Share Document