报告日程

11月2日（周五）上午  主持人：杨静平,王过京    地点：揽秀楼105报告厅
时间	报告人	题目	单位
8:30-8:50	王永进 吴岚 杨静平	开幕致辞	南开大学
8:50-9:30	王永进	The Markov processes potential analysis and American options pricing	南开大学
9:30-10:10	吴岚	金融投资实践中的若干 数学和统计问题	北京大学
10:40-11:20	董迎辉	Optimal asset allocation for participating contracts under trading and VaR constraints	苏州科技大学
11:20-12:00	钱晓松	CDS Pricing in a Markov chain Interacting Intensities model with Contagion	江南·体育(中国区)官方网站
12:00-13:30	午餐
11月2日（周五）下午  主持人：吴岚，王永进   地点：揽秀楼105报告厅
时间	报告人	题目	单位
13:30-14:10	杨静平	CreditRisk+ Model with Dependent Risk Factors	北京大学
14:10-14:50	陈天遥	Decomposing Correlated Random Walks on Common and Counter Movements	北京大学
14:50-15:30	徐玉红	Worst-Case Value at Risk and Portfolio Management: A Simple Method Incorporating Model Uncertainty	江南·体育(中国区)官方网站
16:00-16:40	臧鑫	Unspanned stochastic volatility model for variance swaps	北京大学
16:40-17:20	蒋萍萍	Option pricing under the 4/2 stochastic volatility model with double exponential jumps and stochastic interest rates	南开大学
17:20-18:00	周正雍	Copula-based approximation to Markov chains	北京大学

 

11月3日（周六）上午 专题讨论   主持人 王过京  地点：105报告厅
时间	报告人	题目	单位
8:30-9:00	王永进	互联网金融下信用风险传染问题	南开大学
9:00-9:30	吴岚	互联网金融下现代保险业务结构变化	北京大学
9:30-10:00	杨静平	互联网金融下违约相关风险构造中的数学方法	北京大学
10:00-12:00	自由讨论

 

 

报告摘要

题目：金融投资实践中的若干数学和统计问题

报告人： 吴岚 北京大学数学科学学院

摘要：金融市场投资是金融数学研究的主要问题之一。本报告将提出并与参会者一起讨论在金融量化交易中的两个具体问题以及相关的数学和统计问题：

1、限价或者市价订单簿（book flow）的随机过程模型。在交易数据分析中，要研究几个档位（tick）数据（价量）的时变规律，在成交规则已知的条件下，关于订单簿变化的数学表示目前还未形成公认和可用的模型，该过程比一般的排队模型更加复杂（多规则）且不能假设马氏性。

2、量化策略的绩效度量（IC或者IR）的统计性质和推断问题。量化交易策略的开发和管理中都涉及如何评价绩效的问题，从数学和统计的角度看就是绩效评估变量的概率统计性质的研究。

我们希望通过积极有效的讨论和分享，引起学界对量化投资领域的相关数学问题的研究兴趣、有深入的思考以帮助业界开展有价值的实践。

 

题目：CreditRisk⁺ Model with Dependent Risk Factors

报告人：杨静平 北京大学

摘要：The  model is widely used in industry for computing the loss of a credit portfolio. The standard  model assumes independence among a set of common risk factors, a simplified assumption that leads to computational ease. In this article, we propose to model the common risk factors by a class of multivariate extreme copulas as a generalization of bivariate Fréchet copulas. Further we present a conditional compound Poisson model to approximate the credit portfolio and provide a cost-efficient recursive algorithm to calculate the loss distribution. The new model is more flexible than the standard model, with computational advantages compared to other dependence models of risk factors. It is a joint work with Ruodu Wang and Liang Peng.

 

题目：Optimal asset allocation for participating contracts under trading and VaR constraints

报告人：董迎辉  苏州科技大学

摘要： We investigate an optimal investment problem with trading and VaR constraints faced by the insurer who offers participating contracts. The insurer aims to maximize the expected S-shaped utility of the terminal payoff to the insurer. We adopt a dual control approach and concavification technique to solve the problem and derive the representations of the optimal wealth process and trading strategies. We also carry out some numerical analysis to show how trading and VaR constraints impact the optimal terminal wealth.

 

题目：CDS Pricing in a Markov chain Interacting Intensities model with Contagion

报告人：钱晓松 江南·体育(中国区)官方网站

摘要：We analyze kth-to-default credit default swaps (CDS) with counterparty risk using a markov chain interacting intensities with contagion model. We assume the default intensities of the protection seller and the references are affected by an external shock event and the default intensity of reference entities jump upward when other reference default, The arrival of the shock event is a Cox process whose stochastic intensity is an affine diffusion process with jumps. We examine how the correlated default risks between the protection seller and the underlying entity may affect the credit default premium in a kth-to-default CDS.

 

题目: The Markov processes potential analysis and American options

pricing

报告人：王永进 南开大学

摘要：In this talk, we begin with some theoretical aspects of Markov processes potential analysis. As one of important applications, we will present how super-harmonic functions can be used to solve some optimal stopping problems. This is developing the methods of pricing American options and other early striking available financial contracts.

 

题目：Decomposing Correlated Random Walks on Common and Counter Movements

报告人：陈天遥 北京大学

摘要：Random walk is one of the most classical and well-studied model in probability theory. For two correlated random walks on lattice, every step of the random walks has only two states, moving in the same direction or moving in the opposite direction. This paper presents a decomposition method to study the dependency structure of the two correlated random walks. By applying a change-of-time process, the two random walks can be decomposed into two independent random walks to describe its common movement and its counter movement. A sufficient and necessary condition is given for the mutual independence of the change-of-time process and the two independent random walks.

 

题目：Worst-Case Value at Risk and Portfolio Management: A Simple Method Incorporating Model Uncertainty

报告人：徐玉红 江南·体育(中国区)官方网站

摘要：A kind of worst-case value-at-risk (VaR)-GVaR is defined to measure risk under model uncertainty. Compared with most extant notions of worst-case VaR, GVaR can be computed by explicit formulations, avoiding the usual numerical treatment when facing model uncertainty. It is robust for, but not limited to a set of VaRs based on normal distributions. We also reveal connections to robust portfolio optimization, which provides a tractable way to give optimal allocations under model uncertainty. Empirical analysis demonstrates that GVaR is a robust risk measure. Even for fat-tail returns, GVaR could alleviate the effect brought by fat tail such that it still performs relatively well compared with extant models.

 

题目：Unspanned stochastic volatility model for variance swaps

报告人：臧鑫 北京大学

摘要：Most existing models for volatility derivatives imply that variance swaps or the CBOE VIX span the whole space of volatility risk. However, we find that variance swaps and the VIX have limited explanatory power for VVIX, the CBOE VIX of VIX. We term this feature as unspanned stochastic volatility (USV) for variance swaps, resembling the USV for bonds in the fixed-income market. Thus, we present a new class of canonical-form affine models incorporating such USV factors. Especially, we give a detailed analysis for the classifications of two-factor and three-factor USV models.

 

题目: Option pricing under the 4/2 stochastic volatility model with double exponential jumps and stochastic interest rates

报告人：蒋萍萍 南开大学

摘要：In this talk, we propose a new hybrid stock model, that is 4/2 stochastic volatility model with double exponential jumps and stochastic interest rates.  We derive the explicit expressions for the joint Fourier transform of the interest rate and the log-stock price. Closed- form solutions for European call option prices are derived by applying the inverse Fourier transform.  In the empirical analysis, we estimate the risk-neutral parameters of the model in calibration to both S&P 500 index and option prices. We then evaluate the contribution of stochastic interest rate and jumps in improving the pricing performance. Numerical results demonstrate that our model can fit the SPX prices and make prediction well. We also evaluate its improvement in pricing options with longer maturity. Furthermore, we use the model to examine the effects of jumps and interest rate variability on option values.

 

题目：Copula-based approximation to Markov chains

报告人：周正雍 北京大学

摘要：The construction of Markov chain in views of copula functions is extensively used in time series literatures to model nonlinear temporal dependence. However for many commonly used copula families, dynamics of distributions of the chains are hard to trace. In this paper, we propose the checkerboard copula-based Markov chain to overcome this issue. The explicit form of finite dimensional distributions of the chain are presented. Furthermore, we show the proposed chain can be used as a proper approximation and present error bounds for approximation. As applications, based on results of checkerboard copula-based Markov chains, we obtain a weaker sufficient condition for geometric β-mixing of Markov chains, that allows asymmetry and time-variation in copula functions. Besides, approximate distributions for occupation times and first passage times are also derived under our approximate chain.