A Large Class of Bilateral Distributions for Financial Applications

Khouzeima Moutanabbir () and Houenansi Placide Ezin ()
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Khouzeima Moutanabbir: University of Cape Town
Houenansi Placide Ezin: University of Johannesburg

Methodology and Computing in Applied Probability, 2025, vol. 27, issue 3, 1-29

Abstract: Abstract This paper introduces the new class of Bilateral Mixed Erlang (BME) distributions. Capitalizing on the different properties of the Mixed Erlang distribution, we show that the BME class has some helpful closeness properties, among other interesting characteristics. It also exhibits a high degree of tractability since many quantities of interest, such as the probability density function, the characteristic function, the raw moments, and the expected-shortfall risk measure, are given in closed-form expressions. In this paper, it is shown that the class of BME distributions is dense in the class of all distributions on the real line, which allows the use of BME distributions as an approximation. We also give several examples of distributions that belong to the BME class. In addition to presenting the different properties of this new distribution, we illustrate how this distribution could be used in finance through a few important applications. First, we demonstrate how the BME distribution could approximate other bilateral distributions and their related risk measures, VaR and ES. Then, the BME distribution is applied to fit financial returns, and we assess how it outperforms many other well-known distributions. Also, using an FFT algorithm, we show that this distribution can produce option prices that are volatility-smile consistent with a very good fit to the market options data.

Keywords: Bilateral distributions; Bilateral gamma distributions; Mixed erlang distributions; Option pricing; Fast fourier transform; Expected shortfall risk measure (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11009-025-10193-3

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