Pricing Lookback Options under Normal Inverse Gaussian Model by Variance Reduction and Randomized Quasi-Monte Carlo Methods

2014 ◽  
Author(s):  
Yongzeng Lai ◽  
Jilin Zhang
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Methods ◽  
Variance Reduction ◽  
Gaussian Model ◽  
Inverse Gaussian ◽  
Quasi Monte Carlo ◽  
Lookback Options ◽  
Normal Inverse Gaussian

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

2006 ◽  
Vol 09 (06) ◽  
pp. 843-867 ◽  
Author(s):  
FRED ESPEN BENTH ◽  
MARTIN GROTH ◽  
PAUL C. KETTLER
Keyword(s):  
Monte Carlo ◽  
Value At Risk ◽  
Scale Parameter ◽  
Monte Carlo Algorithm ◽  
Asian Options ◽  
Inverse Gaussian ◽  
Option Prices ◽  
Quasi Monte Carlo ◽  
Normal Inverse Gaussian Distribution ◽  
Normal Inverse Gaussian

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 is based on sampling three independent uniform variables. We apply the algorithm to three problems appearing in finance. First, we consider the valuation of plain vanilla call options and Asian options. The next application considers the problem of deriving implied parameters for the underlying asset dynamics based on observed option prices. We employ our proposed algorithm together with the Newton Method, and show how we can find the scale parameter of the NIG-distribution of the logreturns in case of a call or an Asian option. We also provide an extensive error analysis for this method. Finally we study the calculation of Value-at-Risk for a portfolio of nonlinear products where the returns are modeled by NIG random variables.

Monte Carlo and quasi-Monte Carlo methods

Acta Numerica ◽  
1998 ◽  
Vol 7 ◽  
pp. 1-49 ◽  
Author(s):  
Russel E. Caflisch
Keyword(s):  
Monte Carlo ◽  
Convergence Rate ◽  
Monte Carlo Methods ◽  
Variance Reduction ◽  
Rarefied Gas ◽  
Fluid Dynamic ◽  
Random Sequence ◽  
Convergence Theory ◽  
Quasi Monte Carlo ◽  
Low Discrepancy Sequences

Monte Carlo is one of the most versatile and widely used numerical methods. Its convergence rate, O(N−1/2), is independent of dimension, which shows Monte Carlo to be very robust but also slow. This article presents an introduction to Monte Carlo methods for integration problems, including convergence theory, sampling methods and variance reduction techniques. Accelerated convergence for Monte Carlo quadrature is attained using quasi-random (also called low-discrepancy) sequences, which are a deterministic alternative to random or pseudo-random sequences. The points in a quasi-random sequence are correlated to provide greater uniformity. The resulting quadrature method, called quasi-Monte Carlo, has a convergence rate of approximately O((logN)kN−1). For quasi-Monte Carlo, both theoretical error estimates and practical limitations are presented. Although the emphasis in this article is on integration, Monte Carlo simulation of rarefied gas dynamics is also discussed. In the limit of small mean free path (that is, the fluid dynamic limit), Monte Carlo loses its effectiveness because the collisional distance is much less than the fluid dynamic length scale. Computational examples are presented throughout the text to illustrate the theory. A number of open problems are described.

Variance Reduction for Monte Carlo Methods

2018 ◽  
Vol 482 (6) ◽  
pp. 627-630
Author(s):  
D. Belomestny ◽  
◽  
L. Iosipoi ◽  
N. Zhivotovskiy ◽  
◽  
...  
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Methods ◽  
Variance Reduction

A normal inverse Gaussian model for a risky asset with dependence

2012 ◽  
Vol 82 (1) ◽  
pp. 109-115 ◽  
Author(s):  
N.N. Leonenko ◽  
S. Petherick ◽  
A. Sikorskii
Keyword(s):  
Gaussian Model ◽  
Risky Asset ◽  
Inverse Gaussian ◽  
Normal Inverse Gaussian

scholarly journals Multilevel Quasi-Monte Carlo methods for lognormal diffusion problems

2017 ◽  
Vol 86 (308) ◽  
pp. 2827-2860 ◽  
Author(s):  
Frances Y. Kuo ◽  
Robert Scheichl ◽  
Christoph Schwab ◽  
Ian H. Sloan ◽  
Elisabeth Ullmann
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Methods ◽  
Quasi Monte Carlo ◽  
Diffusion Problems
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