Syeda Rabab Mudakkar

Challenges in the Application of Extreme Value Theory in Emerging Markets: A Case Study of Pakistan

Abstract Application of financial risk models in the emerging markets poses special challenges. A fundamental challenge is to accurately model the return distributions which are particularly fat tailed and skewed. Value-at-Risk (VaR) measures based on the Extreme Value Theory (EVT) have been suggested, but typically data histories are limited, making it hard to test and apply EVT. The chapter addresses issues in (i) modeling the VaR measure in the presence of structural breaks in an economy, (ii) the choice of stable innovation distribution with volatility clustering effects, (iii) modeling the tails of the empirical distribution, and (iv) fixing the cut-off point for isolating extreme observations. Pakistan offers an instructive case since its equity market exhibits high volatility and incidence of extreme returns. The recent Global Financial Crisis has been another source of extreme returns. The confluence of the two sources of volatility provides us with a rich data set to test the VaR/EVT model rigorously and examine practical challenges in its application in an emerging market.

ON STOCHASTIC DOMINANCE OF NILPOTENT OPERATORS

In this paper, motivated by Nica and Speicher [Lectures on the Combinatorics of Free Probability, London Mathematical Society Lecture Note Series, Vol. 335 (Cambridge University Press, 2006)] and Kubo and Kuo [MRM-factors for the probability measures in the Meixner class, Infin. Dimens. Anal. Quantum Probab. Relat. Top.13 (2010) 525–550], we characterize a particular nilpotent case of a truncated forward shift operator by applying the technique of the random walks with repeated reflections and associated renewal equations. We also establish a stochastic order relationship by applying the crossing criteria.

Construction of peculiar diffusion process having Gaussian marginals

ABSTRACT In this note, we construct a new strange diffusion process whose drift coefficient does not satisfy the usual Lipschitz and linear-growth conditions. Beginning with the necessary characteristic equation between drift and diffusion coefficients established in Mudakkar (2012) and using the Foster–Lyapunov criterion and truncation technique, the existence is established.