Abstract : The development of mathematical models used in financial risk management over the past few decades has been remarkable, and it is certainly an area of applied mathematics where many important research topics remain to be explored. This mini-symposium will focus on discussing recent topics related to mathematical methods for quantitative financial risk management. Specifically, topics such as credit risk modeling, applications of stochastic analysis to risk management, risk measures, multivariate statistical modelings, and so on will be presented.
[03276] Discrepancy between Regulations and Practice in Initial Margin Calculation
Format : Talk at Waseda University
Author(s) :
Ryosuke Kitani (Hitotsubashi University)
Hidetoshi Nakagawa (Hitotsubashi University)
Abstract : Counterparty risk remains at issue in OTC derivative transactions. Since it is difficult to calculate the initial margin according to the regulations, it has been calculated in practice using a simplified method "ISDA SIMM". In this study, we derive an approximate formula for some indicators of counterparty risk for a stochastic volatility model and illustrate some numerical analyses to examine the effect of discrepancy between regulations and practice in margin calculation.
[02781] Last Passage Time and its Applications in Risk Management
Format : Talk at Waseda University
Author(s) :
Masahiko Egami (Kyoto University)
Rusudan Kevkhishvili (Kyoto University)
Abstract : We decompose the Laplace transform of a regular transient diffusion’s last passage time into a simple formula based on Green functions. This result allows us to bypass often hard calculations related to diffusions with switching parameters by reducing the problem to two processes without switching. The last passage time is not a stopping time because it looks into the future path of the process. We demonstrate its application in credit risk and loss-given-default distribution modeling.
[04631] Construction and sample path properties of Brownian house-moving
Format : Talk at Waseda University
Author(s) :
Kensuke Ishitani (Tokyo Metropolitan University)
Abstract : We are currently investigating higher-order chain rules for computing higher-order Greeks of barrier options, and we expect a stochastic process called ``Brownian house-moving'' to play an important role in their computation. Brownian house-moving is a Brownian bridge conditioned to stays between two curves. The purpose of this talk is to construct Brownian house-moving. Also studied are the sample path properties of Brownian house-moving.
[02599] Stability of High Order Moments: a Risk Management Approach
Format : Talk at Waseda University
Author(s) :
Olivier Arnaud Le Courtois (emlyon business school)
Silvia Faroni (emlyon business school)
Abstract : Little research has been produced on the statistical reliability of high order moments. This work studies the stability of higher order moments in equity markets. We extend our study to conditional annual higher order moment using different quantiles. Our aim is to identify which moment is more stable over time, which leads to a more reliable assessment of the future market risk and thus to more robust investment and risk management practices.
[03952] Gross-revenue-based structural credit risk model
Format : Talk at Waseda University
Author(s) :
Suguru Yamanaka (Aoyama Gakuin University)
Hidetoshi Nakagawa (Hitotsubashi University)
Abstract : For calculation of firms' default probability, structural models are often used to formulate the stochastic variation of stock variables such as total assets and firm value. In contrast, we propose a new type of structural model based on gross revenue, a flow variable that reflects the income and expenditure of firms. We test the validity of the default probabilities calculated from our proposed model using data on Japanese firms.
[03406] Insider vs. Outsider: Information and Enlargement of Filtrations
Format : Talk at Waseda University
Author(s) :
Kiichi Kitajima (Mitsubishi UFJ Trust Investment Technology Institute Co., Ltd. & Graduate School of Economics, Hitotsubashi University)
Abstract : In this presentation, we introduce a stock price process where a large insider can control the price movement through trading. Under the condition that additional insider information is binary, the study establishes that the information drift is a martingale and that the model has a unique equivalent martingale measure when the insider optimizes their trading. We also characterize the stock's expected return by the insider and an outsider with limited information.
[02711] Sparse factor model of high dimension
Format : Talk at Waseda University
Author(s) :
Benjamin POIGNARD (Osaka University)
Yoshikazu TERADA (Osaka University)
Abstract : We consider the estimation of factor model-based covariance matrix when the factor loading matrix is sparse. We develop a penalized estimating function framework to account for the identifiability of the factor loading matrix while fostering sparsity. We prove the oracle property of the penalized estimator for factor model, that is the penalization can recover the true sparse support and the estimator is asymptotically normal. These theoretical results are supported by simulations and real data experiments.
[03676] On a measure of tail asymmetry for the bivariate skew-normal copula
Format : Talk at Waseda University
Author(s) :
Toshinao Yoshiba (Tokyo Metropolitan University)
Takaaki Koike (Hitotsubashi University)
Shogo Kato (Institute of Statistical Mathematics )
Abstract : Asymmetry in the upper and lower tails is an important feature in modeling financial risk factors. We analyze asymptotic behavior of a measure of tail asymmetry at extremely large and small thresholds of the bivariate skew-normal copula. We numerically show, when the correlation or skewness parameters are around at the boundary values, some proposed asymptotic approximations are not suitable to compute the measure of tail asymmetry.
