Option Pricing and Estimation of Financial Models with R

Iacus, Stefano Maria

doi:10.1002/9781119990079

Cited by 24 publications

(21 citation statements)

References 21 publications

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“…In the first case the quasi-likelihood estimation in Iacus (2011) is considered while, in the second case, the likelihood function is determined as reported in Seneta (2004).…”

Section: It Is Worth Mentioning That the Increments G (R)mentioning

confidence: 99%

COGARCH (p,q) : Simulation and Inference with the yuima Package

Iacus¹,

Mercuri²,

Rroji³

2017

J. Stat. Soft.

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In this paper we show how to simulate and estimate a COGARCH(p, q) model in the R package yuima. Several routines for simulation and estimation are introduced. In particular, for the generation of a COGARCH(p, q) trajectory, the user can choose between two alternative schemes. The first is based on the Euler discretization of the stochastic differential equations that identify a COGARCH(p, q) model while the second considers the explicit solution of the equations defining the variance process.Estimation is based on the matching of the empirical with the theoretical autocorrelation function. Three different approaches are implemented: minimization of the mean squared error, minimization of the absolute mean error and the generalized method of moments where the weighting matrix is continuously updated. Numerical examples are given in order to explain methods and classes used in the yuima package.

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“…In the first case the quasi-likelihood estimation in Iacus (2011) is considered while, in the second case, the likelihood function is determined as reported in Seneta (2004).…”

Section: It Is Worth Mentioning That the Increments G (R)mentioning

confidence: 99%

COGARCH (p,q) : Simulation and Inference with the yuima Package

Iacus¹,

Mercuri²,

Rroji³

2017

J. Stat. Soft.

Self Cite

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“…This comes as no surprise for the reason that Hansen (1982) introduced the GMM primarily with time series applications in mind, and it can be used to obtain parameter estimators that are consistent under weak distributional assumptions (Wooldridge, 2001). The method of moments consists of equating empirical moments with theoretical moments Focardi & Fabozzi (2004) in order to get estimators of the parameters (Iacus, 2011). Chaussé (2010) and Chaussé (2012) thus conclude; because GMM depends only on moment conditions, it is a reliable estimation procedure for many models in economics and finance.…”

Section: Generalised Methods Of Moments (Gmm)mentioning

confidence: 99%

“…The MLE estimates can be heavily biased but asymptotically consistent, efficient, and unbiased for adequately large sample size (Iacus, 2011).…”

Section: Asian Journal Of Finance and Accountingmentioning

confidence: 99%

Generalised Lambda Distributions by Method of Moments and Maximum Likelihood using the JSE-ASI Returns

Owusu

Korkpoe

2017

AJFA

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The four-parameter generalised lambda distribution provides the flexibility required to describe the key moments of any distribution as compared with the normal distribution which characterises the distribution with only two moments. As markets have increasingly become nervous, the inadequacies of the normal distribution in capturing correctly the tail events and describing fully the entire distribution of market returns have been laid bare. The focus of this paper is to compare the generalised method of moments (GMM) and maximum likelihood essential estimates (MLE) methods as subsets of the GLD for a better fit of JSE All Share Index returns data. We have demonstrated that the appropriate method of the GLD to completely describe the measures of central tendency and dispersion by additionally capturing the risk dimensions of skewness and kurtosis of the return distribution is the Generalised Method of Moments (GMM) with the Kolmogorov-Smirnoff Distance good-of-fit statistics and the quantile-quantile graph. These measures are very important to any investor in the equity markets.

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“…Now, we can simulate a sample path of the Homogeneous Gaussian diffusion using the "yuima" package of R language [20]. We use the function "nlm" to compute a value of the estimator.…”

Section: Examplementioning

confidence: 99%

From Nonparametric Density Estimation to Parametric Estimation of Multidimensional Diffusion Processes

N’drin¹,

Hili²

2015

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The paper deals with the estimation of parameters of multidimensional diffusion processes that are discretely observed. We construct estimator of the parameters based on the minimum Hellinger distance method. This method is based on the minimization of the Hellinger distance between the density of the invariant distribution of the diffusion process and a nonparametric estimator of this density. We give conditions which ensure the existence of an invariant measure that admits density with respect to the Lebesgue measure and the strong mixing property with exponential rate for the Markov process. Under this condition, we define an estimator of the density based on kernel function and study his properties (almost sure convergence and asymptotic normality). After, using the estimator of the density, we construct the minimum Hellinger distance estimator of the parameters of the diffusion process and establish the almost sure convergence and the asymptotic normality of this estimator. To illustrate the properties of the estimator of the parameters, we apply the method to two examples of multidimensional diffusion processes.

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Option Pricing and Estimation of Financial Models with R

Cited by 24 publications

References 21 publications

COGARCH (p,q) : Simulation and Inference with the yuima Package

COGARCH (p,q) : Simulation and Inference with the yuima Package

Generalised Lambda Distributions by Method of Moments and Maximum Likelihood using the JSE-ASI Returns

From Nonparametric Density Estimation to Parametric Estimation of Multidimensional Diffusion Processes

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