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.     

How risky is a random process?

The riskiness of random processes is compared by (a) employing a decision theoretic equivalence between processes and lotteries on path-spaces to identify the riskiness of the former with that of the latter, and (b) using the theory of comparative riskiness of lotteries over vector spaces to compare the riskiness of lotteries on a given path-space. We derive the equivalence used in step (a) and contribute a new criterion to the theory applied in step (b). The validity of the new criterion, which applies second order stochastic dominance to utility distributions, is established by showing its equivalence to the benchmark decision theoretic criterion when comparing the riskiness of lotteries over any vector space. We demonstrate the theory’s tractability via diverse economic applications.     

Life-cycle funds: Much Ado about Nothing?

The core idea of life-cycle funds or target-date funds is to decrease the fund's equity exposure and conversely increase its bond exposure towards the fund's target date. Such funds have been gaining significant market share and were recently set as default choice of asset allocation in numerous defined contribution schemes or related old-age provision products in several countries. Hence, an assessment of life-cycle funds’ risk-return profiles – that is, the probability distribution of returns – is essential for sustainable financial planning of a large group of investors. This paper studies the risk-return profile of life-cycle funds in particular compared to simple balanced or lifestyle funds that apply a constant equity portion throughout the fund's term instead. In a Black–Scholes model, we derive balanced funds that reproduce the risk-return profile of an arbitrary life-cycle fund for single and regular contributions. We then analyze the accuracy of our results under more complex asset models with stochastic interest rates, stochastic equity volatility and jumps. We further show that frequently used ‘rule of thumb approximations’ that only take into account the life-cycle fund's average equity portion are not suitable to approximate a life-cycle fund's risk-return profile. Our results on the one hand facilitate sustainable financial planning and on the other hand challenge the very existence of life-cycle funds since appropriately calibrated balanced funds can offer a similar (often dominating) risk-return profile.     

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.     

Optimal transit fare and service frequency of a nonlinear origin-destination based fare structure

This paper proposes a new nonlinear distance-based transit fare structure, which is measured by a function of the Euclidean distance between the origin and destination stations, termed as Origin-Destination (OD)-based fare. The novel fare structure encourages passengers to freely choose the most efficient trip plan. An optimization model is formulated based on a three-party game (involving the transport authority, transit company, and passenger) to determine the optimal fare function and frequency. An artificial bee colony algorithm is adopted to solve the model. Finally, a numerical example is provided to verify the proposed method.     

Optimal investment-consumption-insurance with random parameters

This paper discusses an optimal investment, consumption, and life insurance purchase problem for a wage earner in a complete market with Brownian information. Specifically, we assume that the parameters governing the market model and the wage earner, including the interest rate, appreciation rate, volatility, force of mortality, premium-insurance ratio, income and discount rate, are all random processes adapted to the Brownian motion filtration. Our modeling framework is very general, which allows these random parameters to be unbounded, non-Markovian functionals of the underlying Brownian motion. Suppose that the wage earner’s preference is described by a power utility. The wage earner’s problem is then to choose an optimal investment-consumption-insurance strategy so as to maximize the expected, discounted utilities from intertemporal consumption, legacy and terminal wealth over an uncertain lifetime horizon. We use a novel approach, which combines the Hamilton–Jacobi–Bellman equation and backward stochastic differential equation (BSDE) to solve this problem. In general, we give explicit expressions for the optimal investment-consumption-insurance strategy and the value function in terms of the solutions to two BSDEs. To illustrate our results, we provide closed-form solutions to the problem with stochastic income, stochastic mortality, and stochastic appreciation rate, respectively.     

跳跃随机波动的阈值模型风险值的贝叶斯估计

文章基于一类跳跃随机波动的阈值模型风险值估计贝叶斯分析,在给定先验分布下,以马尔科夫链蒙特卡洛方法估计模型中的未知参数,并给出了MCMC模拟算法,进而讨论了风险值的预测。根据模拟结果,我们得知,如果没有考虑金融时间序列的外生冲击导致的跳跃行为,将会高估风险值,因此考虑跳跃行为后,将增加风险值估计的精度。     

区域要素规模效率及其影响因素的效应机理研究

利用随机前沿超越对数生产函数对我国区域要素规模效率的时变趋势、地域差异进行研究,并通过非效率函数对其宏观影响因素的效应进行了分析。总体看来,考虑影响因素后的效率估计值更为准确：1986—2005年的时变效率在外部环境因素变革的冲击下虽出现了波动情况,但总体上均呈现上升趋势;东部与中西部的效率变化趋势一致,但进入1990年代后东部的平均效率增长速度明显要快于中西部,且效率的东西部推移逐步扩大;另一方面,东西部区域内部的差异均呈现收敛趋势,且东部比中西部区域要显著的多。城市化、工业化、专业化、创新活动、人口素质等因素在不同地域不同发展时期对于效率均体现出不同的影响效应,因而,针对不同地区、发展阶段特征和区域特质其区域政策和发展模式的选择也要有所侧重。     

金融稳定分析的宏观模型综述及展望

金融系统的稳定性水平是金融功能是否有效发挥的反映,加入WTO后中国政府对经济系统进行了诸多方面的改革,金融系统的稳定性得到明显提升,但也存有压力与风险。金融稳定分析的宏观模型包括扩展的宏观经济模型、动态随机一般均衡模型和网络模型。其中,动态随机一般均衡模型具有较好的现实拟合度,应用性较强。应根据中国的社会背景和特殊的金融制度,构建中国特色的动态随机一般均衡模型。     

对话共鸣德育模式的时代意蕴

共振原理为德育共振模式的探讨提供了理论依据,而对话共鸣是实现德育共振的最佳途径。论文主要论述了构建对话共鸣德育模式的依据、原则和途径。