Changes in collateralization have been implicated in significant default (or near-default) events during the financial crisis, most notably with AIG. We have developed a framework for quantifying this effect based on moving between Merton-type and Black-Cox-type structural default models. Our framework leads to a single equation that emcompasses the range of possibilities, including collateralization remargining frequency (i.e. discrete observations). We show that increases in collateralization, by exposing entities to daily mark-to-market volatility, enhance default probability. This quantifies the well-known problem with collateral triggers. Furthermore our model can be used to quantify the degree to which central counterparties, whilst removing credit risk transmission, systematically increase default risk.
A Second Look at Post Crisis Pricing of Derivatives - Part I: A Note on Money Accounts and Collateral
本文回顾了危机后衍生品定价方法的起源，以下三篇论文被从业者广泛接受为理论基础- [Piterbarg 2010]，[Burgard and Kjaer 2010]和[Burgard and Kjaer 2013]。审查表明，这些文件中所采取的方法在概念和技术上存在若干不一致之处。特别是，该方法的一个关键组成部分-为无风险货币账户规定成本组成部分-产生的衍生工具价格没有得到交易衍生工具及其基础证券的市场的清算。它还引入了几个无风险头寸（账户），这些头寸（账户）之间的息差和无风险利率之间的息差持续非零。对于存在交易对手违约风险的衍生品[Burgard and Kjaer 2013]，引入了一种称为半复制的方法，通过对货币账户中的成本成分的选择，衍生品价格产生了以持有交易对手债券组合与持有交易对手债券的衍生品头寸的形式存在的套利机会。有抵押品和无抵押品的高风险衍生品合约，避免这些不一致。
Valuation of Variable Annuities with Equity Protection Swaps under Jumps and Default Risks
School of Mathematics and Statistics, University of Sydney（悉尼大学数学与统计学院）；Faculty of Mathematics and Information Science, Warsaw University of Technology（华沙理工大学数学与信息科学学院）；National University of Singapore, Department of Mathematics（新加坡国立大学数学系）
We introduce the possibility of default in the mean field game of mutual holding of Djete and Touzi [11]. This is modeled by introducing absorption at the origin of the equity process. We provide an explicit solution of this mean field game. Moreover, we provide a particle system approximation, and we derive an autonomous equation for the time evolution of the default probability, or equivalently the law of the hitting time of the origin by the equity process. The systemic risk is thus described by the evolution of the default probability.
Groups of enterprises can serve as guarantees for one another and form complex networks when obtaining loans from commercial banks. During economic slowdowns, corporate default may spread like a virus and lead to large-scale defaults or even systemic financial crises. To help financial regulatory authorities and banks manage the risk associated with networked loans, we identified the default contagion risk, a pivotal issue in developing preventive measures, and established iConVis, an interactive visual analysis tool that facilitates the closed-loop analysis process. A novel financial metric, …
Systemic risks of default contagion in the Russian interbank market are investigated. The analysis is based on considering the bow-tie structure of the weighted oriented graph describing the structure of the interbank loans. A probabilistic model of interbank contagion explicitly taking into account the empirical bow-tie structure reflecting functionality of the corresponding nodes (borrowers, lenders, borrowers and lenders simultaneously), degree distributions and disassortativity of the interbank network under consideration based on empirical data is developed. The characteristics of contagi…
A new procedure is presented for the objective comparison and evaluation of default definitions. This allows the lender to find a default threshold at which the financial loss of a loan portfolio is minimised, in accordance with Basel II. Alternative delinquency measures, other than simply measuring payments in arrears, can also be evaluated using this optimisation procedure. Furthermore, a simulation study is performed in testing the procedure from `first principles' across a wide range of credit risk scenarios. Specifically, three probabilistic techniques are used to generate cash flows, whi…
The modeling of the probability of joint default or total number of defaults among the firms is one of the crucial problems to mitigate the credit risk since the default correlations significantly affect the portfolio loss distribution and hence play a significant role in allocating capital for solvency purposes. In this article, we derive a closed-form expression for the probability of default of a single firm and the probability of the total number of defaults by any time $t$ in a homogeneous portfolio of firms. We use a contagion process to model the arrival of credit events that causes the…
This paper studies the optimal dividend for a multi-line insurance group, in which each subsidiary runs a product line and is exposed to some external credit risk. The default contagion is considered such that one default event may increase the default probabilities of all surviving subsidiaries. The total dividend problem for the insurance group is investigated and we find that the optimal dividend strategy is still of the barrier type. Furthermore, we show that the optimal barrier of each subsidiary is modulated by the default state. That is, how many and which subsidiaries have defaulted wi…
We consider a general tractable model for default contagion and systemic risk in a heterogeneous financial network, subject to an exogenous macroeconomic shock. We show that, under some regularity assumptions, the default cascade model could be transferred to a death process problem represented by balls-and-bins model. We also reduce the dimension of the problem by classifying banks according to different types, in an appropriate type space. These types may be calibrated to real-world data by using machine learning techniques. We then state various limit theorems regarding the final size of de…
Banks and financial institutions all over the world manage portfolios containing tens of thousands of customers. Not all customers are high credit-worthy, and many possess varying degrees of risk to the Bank or financial institutions that lend money to these customers. Hence assessment of credit risk is paramount in the field of credit risk management. This paper discusses the use of Bayesian principles and simulation-techniques to estimate and calibrate the default probability of credit ratings. The methodology is a two-phase approach where, in the first phase, a posterior density of default …
A standard quantitative method to access credit risk employs a factor model based on joint multivariate normal distribution properties. By extending a one-factor Gaussian copula model to make a more accurate default forecast, this paper proposes to incorporate a state-dependent recovery rate into the conditional factor loading, and model them by sharing a unique common factor. The common factor governs the default rate and recovery rate simultaneously and creates their association implicitly. In accordance with Basel III, this paper shows that the tendency of default is more governed by system…
