RECOVERING PORTFOLIO DEFAULT INTENSITIES IMPLIED BY CDO QUOTES

We propose a stable nonparametric algorithm for the calibration of “top‐down” pricing models for portfolio credit derivatives: given a set of observations of market spreads for collateralized debt obligation (CDO) tranches, we construct a risk‐neutral default intensity process for the portfolio underlying the CDO which matches these observations, by looking for the risk‐neutral loss process “closest” to a prior loss process, verifying the calibration constraints. We formalize the problem in terms of minimization of relative entropy with respect to the prior under calibration constraints and use convex duality methods to solve the problem: the dual problem is shown to be an intensity control problem, characterized in terms of a Hamilton–Jacobi system of differential equations, for which we present an analytical solution. Given a set of observed CDO tranche spreads, our method allows to construct a default intensity process which leads to tranche spreads consistent with the observations. We illustrate our method on ITRAXX index data: our results reveal strong evidence for the dependence of loss transitions rates on the previous number of defaults, and offer quantitative evidence for contagion effects in the (risk‐neutral) loss process.     

MULTIDIMENSIONAL DYNAMIC RISK MEASURE VIA CONDITIONAL g‐EXPECTATION

This paper deals with multidimensional dynamic risk measures induced by conditional g‐expectations. A notion of multidimensional g‐expectation is proposed to provide a multidimensional version of nonlinear expectations. By a technical result on explicit expressions for the comparison theorem, uniqueness theorem, and viability on a rectangle of solutions to multidimensional backward stochastic differential equations, some necessary and sufficient conditions are given for the constancy, monotonicity, positivity, and translatability properties of multidimensional conditional g‐expectations and multidimensional dynamic risk measures; we prove that a multidimensional dynamic g‐risk measure is nonincreasingly convex if and only if the generator g satisfies a quasi‐monotone increasingly convex condition. A general dual representation is given for the multidimensional dynamic convex g‐risk measure in which the penalty term is expressed more precisely. It is shown that model uncertainty leads to the convexity of risk measures. As to applications, we show how this multidimensional approach can be applied to measure the insolvency risk of a firm with interacting subsidiaries; optimal risk sharing for ‐tolerant g‐risk measures, and risk contribution for coherent g‐risk measures are investigated. Insurance g‐risk measure and other ways to induce g‐risk measures are also studied at the end of the paper.     

VALUATION OF BARRIER OPTIONS VIA A GENERAL SELF‐DUALITY

Classical put–call symmetry relates the price of puts and calls under a suitable dual market transform. One well‐known application is the semistatic hedging of path‐dependent barrier options with European options. This, however, in its classical form requires the price process to observe rather stringent and unrealistic symmetry properties. In this paper, we develop a general self‐duality theorem to develop valuation schemes for barrier options in stochastic volatility models with correlation.     

No Arbitrage in Discrete Time Under Portfolio Constraints

In frictionless securities markets, the characterization of the no-arbitrage condition by the existence of equivalent martingale measures in discrete time is known as the fundamental theorem of asset pricing. In the presence of convex constraints on the trading strategies, we extend this theorem under a closedness condition and a nondegeneracy assumption. We then provide connections with the superreplication problem solved in Föllmer and Kramkov (1997).     

ARBITRAGE‐FREE BILATERAL COUNTERPARTY RISK VALUATION UNDER COLLATERALIZATION AND APPLICATION TO CREDIT DEFAULT SWAPS

We develop an arbitrage‐free valuation framework for bilateral counterparty risk, where collateral is included with possible rehypothecation. We show that the adjustment is given by the sum of two option payoff terms, where each term depends on the netted exposure, i.e., the difference between the on‐default exposure and the predefault collateral account. We then specialize our analysis to credit default swaps (CDS) as underlying portfolios, and construct a numerical scheme to evaluate the adjustment under a doubly stochastic default framework. In particular, we show that for CDS contracts a perfect collateralization cannot be achieved, even under continuous collateralization, if the reference entity’s and counterparty’s default times are dependent. The impact of rehypothecation, collateral margining frequency, and default correlation‐induced contagion is illustrated with numerical examples.     

PRICING DERIVATIVES ON MULTISCALE DIFFUSIONS: AN EIGENFUNCTION EXPANSION APPROACH

Using tools from spectral analysis, singular and regular perturbation theory, we develop a systematic method for analytically computing the approximate price of a large class of derivative‐assets. The payoff of the derivative‐assets may be path‐dependent. In addition, the process underlying the derivatives may exhibit killing (i.e., jump to default) as well as combined local/nonlocal stochastic volatility. The nonlocal component of volatility may be multiscale, in the sense that it may be driven by one fast‐varying and one slow‐varying factor. The flexibility of our modeling framework is contrasted by the simplicity of our method. We reduce the derivative pricing problem to that of solving a single eigenvalue equation. Once the eigenvalue equation is solved, the approximate price of a derivative can be calculated formulaically. To illustrate our method, we calculate the approximate price of three derivative‐assets: a vanilla option on a defaultable stock, a path‐dependent option on a nondefaultable stock, and a bond in a short‐rate model.     

Robust consumption‐investment problem under CRRA and CARA utilities with time‐varying confidence sets

We consider a robust consumption‐investment problem under constant relative risk aversion and constant absolute risk aversion utilities. The time‐varying confidence sets are specified by Θ, a correspondence from [0, T] to the space of the Lévy triplets, and describe a priori drift, volatility, and jump information. For each possible measure, the log‐price processes of stocks are semimartingales, and the triplet of their differential characteristics is almost surely a measurable selector from the correspondence Θ. By proposing and investigating the global kernel, an optimal policy and a worst‐case measure are generated from a saddle point of the global kernel, and they constitute a saddle point of the objective function.     

Inference for large financial systems

We treat the parameter estimation problem for mean‐field models of large interacting financial systems such as the banking system and a pool of assets held by an institution or backing a security. We develop an asymptotic inference approach that addresses the scale and complexity of such systems. Harnessing the weak convergence results developed for mean‐field financial systems in the literature, we construct an approximate likelihood for large systems. The approximate likelihood has a conditionally Gaussian structure, enabling us to design an efficient numerical method for its evaluation. We provide a representation of the corresponding approximate estimator in terms of a weighted least‐squares estimator, and use it to analyze the large‐system and large‐sample behavior of the estimator. Numerical results for a mean‐field model of systemic financial risk highlight the efficiency and accuracy of our estimator.     

利用ACE值构造QC-LDPC码

为进一步提升中短码长下准循环低密度奇偶校验(Quasi-cyclic Low-density Parity-check,QC-LDPC) 码的纠错性能,提出了一种综合短环数目和环连通性的QC-LDPC码构造方法。首先,采用Golomb规则构造QC-LDPC码,对基矩阵中的部分元素进行替换预处理,初步降低短环数目;其次,采用所提的利用近似环外信息度（Approximate Cycle Extrinsic message degree,ACE）的消环掩模算法来优化QC-LDPC码,使得掩模后的校验矩阵具有较大的ACE平均值,最终完成QC-LDPC码的构造。该构造方法简单、通用性强,在短环数目和连通性间进行了平衡。与只考虑减少短环数目、增大围长等方法相比,该方法构造的QC-LDPC码有更加优异的纠错性能。     

Heterogeneity and netting efficiency under central clearing: A stochastic network analysis

This paper examines the effect of heterogeneity in clearing members’ exposure management practices under central clearing. Our network model specifies the dynamics of prenetted interbank exposures to shape interdependent exposure distributions beyond normality. Employing over-the-counter derivatives market data from the U.S. Office of the Comptroller of the Currency, our simulation results indicate that heterogeneity in bank-to-bank exposure dynamics is systemically desirable, while the entire system benefits more from the central clearing in more homogeneous environments. Policymakers should incentivize individual clearing members to enhance resiliency and stability in counterparty exposure management to maximize netting efficiency under central clearing.