High-order computational methods for option valuation under multifactor models

Rambeerich, Nisha; Tangman, Désiré Yannick; Lollchund, Michel Roddy; Bhuruth, Muddun

doi:10.1016/j.ejor.2012.07.023

Cited by 29 publications

(30 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finally the proposed factorization has potential and immediate applications to the study of properties of discrete time Markov Chains as well, a very important topic in operational research for modeling queuing sequences and many other practical systems, see [29]. Extension to other processes, as normal mixture distribution, see [5], and options with multiple risk factors, such as stochastic volatility models or multi-assets contracts, as in [9,24,33], are also amenable to the presented technique, and will be treated in a follow-up paper.…”

Section: Resultsmentioning

confidence: 99%

Pricing exotic derivatives exploiting structure

Sesana

Marazzina

Fusai

2014

European Journal of Operational Research

View full text Add to dashboard Cite

This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link AbstractIn this paper we introduce a new fast and accurate numerical method for pricing exotic derivatives when discrete monitoring occurs, and the underlying evolves according to a Markov one-dimensional stochastic processes. The approach exploits the structure of the matrix arising from the numerical quadrature of the pricing backward formulas to devise a convenient factorization that helps greatly in the speed-up of the recursion. The algorithm is general and is examined in detail with reference to the CEV (Constant Elasticity of Variance) process for pricing different exotic derivatives, such as Asian, barrier, Bermudan, lookback and step options for which up to date no efficient procedures are available. Extensive numerical experiments confirm the theoretical results. The MATLAB code used to perform the computation is available online at

show abstract

Section: Resultsmentioning

confidence: 99%

Pricing exotic derivatives exploiting structure

Sesana

Marazzina

Fusai

2014

European Journal of Operational Research

View full text Add to dashboard Cite

show abstract

“…Beginning in 1973, it was described that a mathematical framework for finding the fair price of a European option by Black and Scholes [1,2], several numerical methods have been presented for the cases where analytic solutions are neither available nor easily computable. See more details about numerical methods such as finite difference method (FDM) [3,4,5,6,7,8,9,10,11,12,13], finite element method [14,15,16], finite volume method [17,18,19], and a fast Fourier transform [20,21,22,23,24]. For convenience, we use the closed-form of the Black-Scholes equation in this work.…”

Section: Introductionmentioning

confidence: 99%

Path Averaged Option Value Criteria for Selecting Better Options

Kim¹,

Yoo²,

Son³

et al. 2016

Journal of the Korea Society for Industrial and Applied Mathema

View full text Add to dashboard Cite

ABSTRACT. In this paper, we propose an optimal choice scheme to determine the best option among comparable options whose current expectations are all the same under the condition that an investor has a confidence in the future value realization of underlying assets. For this purpose, we use a path-averaged option as our base instrument in which we calculate the time discounted value along the path and divide it by the number of time steps for a given expected path. First, we consider three European call options such as vanilla, cash-or-nothing, and assetor-nothing as our comparable set of choice schemes. Next, we perform the experiments using historical data to prove the usefulness of our proposed scheme. The test suggests that the pathaveraged option value is a good guideline to choose an optimal option.

show abstract

“…With respect to the numerical treatment of the integral part of the PIDE problem we use a different approach of those developed in [5] and [8]. In fact,…”

Section: Introductionmentioning

confidence: 99%

“…More recently the authors in [8] employ high-order Galerkin finite element 25 discretizations for both two asset option pricing problems and stochastic volatility models. The resulting semi-discrete systems are solved using exponential time integration.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical valuation of two-asset options under jump diffusion models using Gauss–Hermite quadrature

Fakharany

Egorova

2018

Journal of Computational and Applied Mathematics

View full text Add to dashboard Cite

In this work a finite difference approach together with a bivariate Gauss-Hermite quadrature technique are developed for partial-integro differential equations related to option pricing problems on two underlying asset driven by jumpdiffusion models. Firstly, the mixed derivative term is removed using a suitable transformation avoiding numerical drawbacks such as slow convergence and inaccuracy due to the appearance of spurious oscillations. Unlike the more traditional truncation approach we use 2D Gauss-Hermite quadrature with the additional advantage of saving computational cost. The explicit finite difference scheme becomes consistent, conditionally stable and positive. European and American option cases are treated. Numerical results are illustrated and analyzed with experiments and comparisons with other well recognized methods.

show abstract

High-order computational methods for option valuation under multifactor models

Cited by 29 publications

References 21 publications

Pricing exotic derivatives exploiting structure

Pricing exotic derivatives exploiting structure

Path Averaged Option Value Criteria for Selecting Better Options

Numerical valuation of two-asset options under jump diffusion models using Gauss–Hermite quadrature

Contact Info

Product

Resources

About