Statistical Models in Finance and Insurance

Abstract

The special issue of Model Assisted Statistics and Applications, 12 (4) 2017, is dedicated to Statistical Models in Finance and Insurance. As Guest Editors, we would like to introduce seven papers comprising the issue and present the unifying ideas explaining the choice of the content.Our goal for the special issue is offering to the readers a variety of topics representing a wide range of applications of statistical methods to insurance and finance, requiring new methodological approaches. Classical development of financial and actuarial mathematics in the 20-th century including such fundamental achievements as Markowitz model, CAPM, Black-Scholes formula, Buhlmann's credibility theory, CDO pricing using Gaussian copulas and others, was effectively based on mean and covariance, thus, heavily relying on accuracy of an open or hidden assumption of normality of underlying variables. Statistical analysis of financial variables emphasized the estimation of distribution moments, and the study of dependence between variables was mostly reduced to correlation analysis. This approach worked successfully for a while. However, one of the principal challenges of financial and insurance risk modeling is an extreme fluidity of their universe, at least in comparison with the surrounding physical world. When market agents trust the modeling assumptions, models work. When this trust is shaken, models cease to reflect the reality. Realities of the last decades and the turn of the 20-th century in a most painful way demonstrated the inadequacy of the classical approach and a need for new developments. The new financial environment called for a new mathematical and statistical methodology. Introducing asymmetric and tail-heavy distribution models for risk variables and going beyond correlation in description of their association becomes a staple of modern quantitative analysis. Therefore, the emphasis in this issue is made on the modern understanding of financial and insurance practice beyond the standard set of assumptions requiring normality of key modeling variables. It calls for the development of new methods under somewhat more complicated assumptions reflecting a more realistic view of the financial and insurance world.We introduce seven papers, with the order of a particular article suggested by similarity of applications rather than by a particular statistical technique.The two opening articles deal with the models of market risks reflecting the realities of post-Black-Scholes statistical methods. The first paper by Chung and Niu "Financial Volatility Estimation Using Functional Gradient Descent Algorithm" introduces a new semiparametric model of volatility in financial time series, presenting an alternative to existing stochastic volatility models. De Lara-Tuprio and Sumalpong in "British Put Option on Stock under Stochastic Interest Rate" derive a closed-form pricing formula under stochastic interest rate (Vasicek model), while previous results are confined to constant interest rate. Assuming the stochastic nature of vo...