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ScienceAsia 48 (2022): 240-246 |doi: 10.2306/scienceasia1513-1874.2022.033

Normal approximation for call function of locally dependent random variables

Suporn Jongpreechaharn, Kritsana Neammaneea,b,*

ABSTRACT:     A mean for the call function of random variable W, E(W ? k) + , where k is a positive real number, is useful and important, for instance, in a collateralized debt obligation (CDO) tranche pricing. In previous works, E(W ? k) + is approximated by normal approximation where W is a sum of independent random variables. However, W in this paper is extended to be a sum of locally dependent random variables. We propose a uniform bound on the normal approximation by using the Stein?s method.

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a Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330 Thailand
b Centre of Excellence in Mathematics, Commission on Higher Education, Bangkok, Thailand

* Corresponding author, E-mail: kritsana.n@chula.ac.th

Received 7 Jun 2021, Accepted 29 Nov 2021