DSpace collection: 期刊論文

Unbiased and efficient Greeks of financial options

title: Unbiased and efficient Greeks of financial options abstract: The price of a derivative security equals the discounted expected payoff of the security under a suitable measure, and Greeks are price sensitivities with respect to parameters of interest. When closed-form formulas do not exist, Monte Carlo simulation has proved very useful for computing the prices and Greeks of derivative securities. Although finite difference with resimulation is the standard method for estimating Greeks, it is in general biased and suffers from erratic behavior when the payoff function is discontinuous. Direct methods, such as the pathwise method and the likelihood ratio method, are proposed to differentiate the price formulas directly and hence produce unbiased Greeks (Broadie and Glasserman, Manag. Sci. 42:269-285, 1996). The pathwise method differentiates the payoff function, whereas the likelihood ratio method differentiates the densities. When both methods apply, the pathwise method generally enjoys lower variances, but it requires the payoff function to be Lipschitz-continuous. Similarly to the pathwise method, our method differentiates the payoff function but lifts the Lipschitz-continuity requirements on the payoff function. We build a new but simple mathematical formulation so that formulas of Greeks for a broad class of derivative securities can be derived systematically. We then present an importance sampling method to estimate the Greeks. These formulas are the first in the literature. Numerical experiments show that our method gives unbiased Greeks for several popular multi-asset options (also called rainbow options) and a path-dependent option.

Robust likelihood inferences for multivariate correlated data

title: Robust likelihood inferences for multivariate correlated data abstract: Multivariate normal, due to its well-established theories, is commonly utilized to analyze correlated data of various types. However, the validity of the resultant inference is, more often than not, erroneous if the model assumption fails. We present a modification for making the multivariate normal likelihood acclimatize itself to general correlated data. The modified likelihood is asymptotically legitimate for any true underlying joint distributions so long as they have finite second moments. One can, hence, acquire full likelihood inference without knowing the true random mechanisms underlying the data. Simulations and real data analysis are provided to demonstrate the merit of our proposed parametric robust method.

Robust likelihood inference for regression parameters in partially linear models

title: Robust likelihood inference for regression parameters in partially linear models abstract: A robust likelihood approach is proposed for inference about regression parameters in partially-linear models. More specifically, normality is adopted as the working model and is properly corrected to accomplish the objective. Knowledge about the true underlying random mechanism is not required for the proposed method. Simulations and illustrative examples demonstrate the usefulness of the proposed robust likelihood method, even in irregular situations caused by the components of the nonparametric smooth function in partially-linear models. (C) 2010 Elsevier B.V. All rights reserved.

Likelihood inferences for the link function without knowing the true underlying distributions

title: Likelihood inferences for the link function without knowing the true underlying distributions abstract: This article is concerned with inference about link function in generalized linear models. A parametric and yet robust likelihood approach is introduced to accomplish the intended goal. More specifically, it is demonstrated that one can convert normal and gamma likelihoods into robust likelihood functions for the link function. The asymptotic validity of the robust likelihood requires only the existence of the second moments of the underlying distributions. The application of this novel robust likelihood method is demonstrated on the Box-Cox transformation. Simulation studies and real data analysis are provided to demonstrate the efficacy of the new parametric robust procedures.