Restructuring risk in credit default swaps: An empirical analysis

This paper estimates the price for restructuring risk in the US corporate bond market during 1999–2005. Comparing quotes from default swap (CDS) contracts with a restructuring event and without, we find that the average premium for restructuring risk represents 6%–8% of the swap rate without restructuring. We show that the restructuring premium depends on firm-specific balance-sheet and macroeconomic variables. And, when default swap rates without a restructuring event increase, the increase in restructuring premia is higher for low-credit-quality firms than for high-credit-quality firms. We propose a reduced-form arbitrage-free model for pricing default swaps that explicitly incorporates the distinction between restructuring and default events. A case study illustrating the model’s implementation is provided.     

A model for dependent default with hyperbolic attenuation effect and valuation of credit default swap

A hyperbolic function is introduced to reflect the attenuation effect of one firm's default to its partner.If two firms are competitors(copartners),the default inten- sity of one firm will decrease(increase)abruptly when the other firm defaults.As time goes on,the impact will decrease gradually until extinct.In this model,the joint distri- bution and marginal distributions of default times are derived by employing the change of measure,and the fair swap premium of a credit default swap(CDS)can be valued.     

Robust equilibrium excess-of-loss reinsurance and CDS investment strategies for a mean–variance insurer with ambiguity aversion

This paper considers the robust equilibrium reinsurance and investment strategies for an ambiguity-averse insurer under a dynamic mean–variance criterion. The insurer is allowed to purchase excess-of-loss reinsurance and invest in a financial market consisting of a risk-free asset and a credit default swap (CDS). Following a game theoretic approach, robust equilibrium strategies and equilibrium value functions for the pre-default case and the post-default case are derived, respectively. For the ambiguity-averse insurer, in general the equilibrium strategies can be characterized by unique solutions to some algebraic equations. For the degenerate case with an ambiguity-neutral insurer, closed-form expressions of equilibrium strategies and equilibrium value functions are obtained. Numerical examples demonstrate that the consideration of model uncertainty and CDS investment improves the insurer’s utility. In this regard, our paper establishes theoretical and numerical support for the importance of ambiguity aversion, credit risk and their interplay in insurance business.     

Optimal consumption and investment with insurer default risk

We solve the optimal consumption and investment problem in an incomplete market, where borrowing constraints and insurer default risk are considered jointly. We derive in closed-form the optimal consumption and investment strategies. We find two main results by quantitative analysis. As insurer default risk increases, the proportion of wealth invested in stocks could increase when wealth is small, and decrease when wealth is large. As risk aversion increases, the voluntary annuity demand could increase when insurer default risk is low, and decrease when this risk is high.     

基于博弈论的融资租赁保证金确定方法研究

针对融资租赁中租金偿还违约风险的防范问题,研究了如何合理设置租赁保证金来防范违约风险.运用博弈理论建立了租金偿还的动态博弈模型,采用逆向归纳法求解该博弈模型并推导出了预防性保证金确定方法及其适用条件,通过边界条件的改变继而推导出了补偿性保证金确定方法及其适用条件.算例分析表明,运用两种方法来计算租赁保证金时,只需已知租赁项目各期租金和租赁资产的价值而无需知道租赁项目的各期收益,仅以出租人预期租赁项目在各期的收益与租金之间的大小作为判据来选择保证金确定方法.两种保证金确定方法具有较高的实用性和可操作性,是出租人合理地确定租赁保证金的有效方法.     

Perpetual convertible bonds with credit risk

A convertible bond is a security that the holder can convert into a specified number of underlying shares. We enrich the standard model by introducing some default risk of the issuer. Once default has occured payments stop immediately. In the context of a reduced form model with infinite time horizon driven by a Brownian motion, analytical formulae for the no-arbitrage price of this American contingent claim are obtained and characterised in terms of solutions of free boundary problems. It turns out that the default risk changes the structure of the optimal stopping strategy essentially. Especially, the continuation region may become a disconnected subset of the state space.     

A dynamic binomial expansion technique for credit risk measurement: a Bayesian filtering approach

Credit risk measurement and management are important and current issues in the modern finance world from both the theoretical and practical perspectives. There are two major schools of thought for credit risk analysis, namely the structural models based on the asset value model originally proposed by Merton and the intensity‐based reduced form models. One of the popular credit risk models used in practice is the Binomial Expansion Technique (BET) introduced by Moody's. However, its one‐period static nature and the independence assumption for credit entities' defaults are two shortcomings for the use of BET in practical situations. Davis and Lo provided elegant ways to ease the two shortcomings of BET with their default infection and dynamic continuous‐time intensity‐based approaches. This paper first proposes a discrete‐time dynamic extension to the BET in order to incorporate the time‐dependent and time‐varying behaviour of default probabilities for measuring the risk of a credit risky portfolio. In reality, the ‘true’ default probabilities are unobservable to credit analysts and traders. Here, the uncertainties of ‘true’ default probabilities are incorporated in the context of a dynamic Bayesian paradigm. Numerical studies of the proposed model are provided.     

A Multivariate Regime-Switching Mean Reverting Process and Its Application to the Valuation of Credit Risk

In this article, we study the counterparty risk on a credit default swap (CDS) and the valuation of a first-to-default basket swap on three underlyings under a common shock model with regime-switching intensities. We assume that the defaults of all the names are driven by some shock events, whose arrivals are governed by a multivariate regime-switching shot noise process. Based on some expressions for the joint Laplace transform of the regime-switching shot noise processes, we give explicit formulas for the spread of the CDS contract with and without counterparty risk and the spread of the first-to-default basket swap on the three underlyings.     

随机波动率模型下含违约风险的欧式衍生产品的套期保值

研究了含违约风险的欧式未定权益的最优套期保值问题. 假定含违约风险衍生产品的标的资产满足Heston随机波动率模型, 则利用局部风险最小化方法获得含违约风险衍生产品的最优套期保值策略. 此外, 还考虑了在一个特别情况下, 研究了含违约风险的欧式看涨期权的最优套期保值问题, 并通过特征函数和傅里叶反演公式给出了明确的局部风险最小化套期保值策略.