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Optimal Expected-Shortfall Portfolio Selection with Copula-Induced Dependence 具有copula诱导依赖的最优预期亏损投资组合选择
Applied Mathematical Finance Pub Date : 2018-01-02 DOI: 10.1080/1350486X.2018.1492347
I. Gijbels, K. Herrmann
{"title":"Optimal Expected-Shortfall Portfolio Selection with Copula-Induced Dependence","authors":"I. Gijbels, K. Herrmann","doi":"10.1080/1350486X.2018.1492347","DOIUrl":"https://doi.org/10.1080/1350486X.2018.1492347","url":null,"abstract":"ABSTRACT We provide a computational framework for the selection of weights that minimize the expected shortfall of the aggregated risk . Contrary to classic and recent results, we neither restrict the marginal distributions nor the dependence structure of to any specific type. While the margins can be set to any absolutely continuous random variable with finite expectation, the dependence structure can be modelled by any absolutely continuous copula function. A real-world application to portfolio selection illustrates the usability of the new framework.","PeriodicalId":35818,"journal":{"name":"Applied Mathematical Finance","volume":"8 1","pages":"106 - 66"},"PeriodicalIF":0.0,"publicationDate":"2018-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74492199","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Transition Probability of Brownian Motion in the Octant and its Application to Default Modelling 布朗运动在八分区中的转移概率及其在默认建模中的应用
Applied Mathematical Finance Pub Date : 2017-12-01 DOI: 10.1080/1350486X.2018.1481439
Vadim Kaushansky, A. Lipton, C. Reisinger
{"title":"Transition Probability of Brownian Motion in the Octant and its Application to Default Modelling","authors":"Vadim Kaushansky, A. Lipton, C. Reisinger","doi":"10.1080/1350486X.2018.1481439","DOIUrl":"https://doi.org/10.1080/1350486X.2018.1481439","url":null,"abstract":"ABSTRACT We derive a semi-analytical formula for the transition probability of three-dimensional Brownian motion in the positive octant with absorption at the boundaries. Separation of variables in spherical coordinates leads to an eigenvalue problem for the resulting boundary value problem in the two angular components. The main theoretical result is a solution to the original problem expressed as an expansion into special functions and an eigenvalue which has to be chosen to allow a matching of the boundary condition. We discuss and test several computational methods to solve a finite-dimensional approximation to this nonlinear eigenvalue problem. Finally, we apply our results to the computation of default probabilities and credit valuation adjustments in a structural credit model with mutual liabilities.","PeriodicalId":35818,"journal":{"name":"Applied Mathematical Finance","volume":"4 4","pages":"434 - 465"},"PeriodicalIF":0.0,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1350486X.2018.1481439","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72488487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Two asset-barrier option under stochastic volatility 随机波动下的两种资产障碍期权
Applied Mathematical Finance Pub Date : 2017-11-02 DOI: 10.1080/1350486X.2017.1419910
Barbara Goetz, M. Escobar, R. Zagst
{"title":"Two asset-barrier option under stochastic volatility","authors":"Barbara Goetz, M. Escobar, R. Zagst","doi":"10.1080/1350486X.2017.1419910","DOIUrl":"https://doi.org/10.1080/1350486X.2017.1419910","url":null,"abstract":"ABSTRACT Financial products which depend on hitting times for two underlying assets have become very popular in the last decade. Three common examples are double-digital barrier options, two-asset barrier spread options and double lookback options. Analytical expressions for the joint distribution of the endpoints and the maximum and/or minimum values of two assets are essential in order to obtain quasi-closed form solutions for the price of these derivatives. Earlier authors derived quasi-closed form pricing expressions in the context of constant volatility and correlation. More recently solutions were provided in the presence of a common stochastic volatility factor but with restricted correlations due to the use of a method of images. In this article, we generalize this finding by allowing any value for the correlation. In this context, we derive closed-form expressions for some two-asset barrier options.","PeriodicalId":35818,"journal":{"name":"Applied Mathematical Finance","volume":"34 1","pages":"520 - 546"},"PeriodicalIF":0.0,"publicationDate":"2017-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80925344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
A Mathematical Analysis of Technical Analysis 技术分析的数学分析
Applied Mathematical Finance Pub Date : 2017-10-25 DOI: 10.1080/1350486X.2019.1588136
Matthew J. Lorig, Zhou Zhou, B. Zou
{"title":"A Mathematical Analysis of Technical Analysis","authors":"Matthew J. Lorig, Zhou Zhou, B. Zou","doi":"10.1080/1350486X.2019.1588136","DOIUrl":"https://doi.org/10.1080/1350486X.2019.1588136","url":null,"abstract":"ABSTRACT In this paper, we investigate trading strategies based on exponential moving averages (ExpMAs) of an underlying risky asset. We study both logarithmic utility maximization and long-term growth rate maximization problems and find closed-form solutions when the drift of the underlying is modelled by either an Ornstein-Uhlenbeck process or a two-state continuous-time Markov chain. For the case of an Ornstein-Uhlenbeck drift, we carry out several Monte Carlo experiments in order to investigate how the performance of optimal ExpMA strategies is affected by variations in model parameters and by transaction costs.","PeriodicalId":35818,"journal":{"name":"Applied Mathematical Finance","volume":"46 1","pages":"38 - 68"},"PeriodicalIF":0.0,"publicationDate":"2017-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86644791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Short Maturity Forward Start Asian Options in Local Volatility Models 本地波动率模型下的短期远期启动亚洲期权
Applied Mathematical Finance Pub Date : 2017-10-09 DOI: 10.1080/1350486X.2019.1584533
D. Pirjol, Jing Wang, Lingjiong Zhu
{"title":"Short Maturity Forward Start Asian Options in Local Volatility Models","authors":"D. Pirjol, Jing Wang, Lingjiong Zhu","doi":"10.1080/1350486X.2019.1584533","DOIUrl":"https://doi.org/10.1080/1350486X.2019.1584533","url":null,"abstract":"ABSTRACT We study the short maturity asymptotics for prices of forward start Asian options under the assumption that the underlying asset follows a local volatility model. We obtain asymptotics for the cases of out-of-the-money, in-the-money, and at-the-money, considering both fixed strike and floating Asian options. The exponential decay of the price of an out-of-the-money forward start Asian option is handled using large deviations theory, and is controlled by a rate function which is given by a double-layer optimization problem. In the Black-Scholes model, the calculation of the rate function is simplified further to the solution of a non-linear equation. We obtain closed form for the rate function, as well as its asymptotic behavior when the strike is extremely large, small, or close to the initial price of the underlying asset.","PeriodicalId":35818,"journal":{"name":"Applied Mathematical Finance","volume":"4 1","pages":"187 - 221"},"PeriodicalIF":0.0,"publicationDate":"2017-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82148040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Polynomial Processes for Power Prices 电价的多项式过程
Applied Mathematical Finance Pub Date : 2017-10-01 DOI: 10.2139/ssrn.3170978
T. Ware
{"title":"Polynomial Processes for Power Prices","authors":"T. Ware","doi":"10.2139/ssrn.3170978","DOIUrl":"https://doi.org/10.2139/ssrn.3170978","url":null,"abstract":"ABSTRACT Polynomial processes have the property that expectations of polynomial functions (of degree n, say) of the future state of the process conditional on the current state are given by polynomials (of degree ≤ n) of the current state. Here we explore the potential of polynomial maps of polynomial processes for modelling energy prices. We focus on the example of Alberta power prices, derive one- and two-factor models for spot prices. We examine their performance in numerical experiments, and demonstrate that the richness of the dynamics they are able to generate makes them well suited for modelling even extreme examples of energy price behaviour.","PeriodicalId":35818,"journal":{"name":"Applied Mathematical Finance","volume":"36 4 1","pages":"453 - 474"},"PeriodicalIF":0.0,"publicationDate":"2017-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90459955","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 20
Counterparty Credit Limits: The Impact of a Risk-Mitigation Measure on Everyday Trading 交易对手信用限额:风险缓解措施对日常交易的影响
Applied Mathematical Finance Pub Date : 2017-09-24 DOI: 10.1080/1350486X.2021.1893770
M. Gould, N. Hautsch, S. Howison, M. A. Porter
{"title":"Counterparty Credit Limits: The Impact of a Risk-Mitigation Measure on Everyday Trading","authors":"M. Gould, N. Hautsch, S. Howison, M. A. Porter","doi":"10.1080/1350486X.2021.1893770","DOIUrl":"https://doi.org/10.1080/1350486X.2021.1893770","url":null,"abstract":"ABSTRACT A counterparty credit limit (CCL) is a limit that is imposed by a financial institution to cap its maximum possible exposure to a specified counterparty. CCLs help institutions to mitigate counterparty credit risk via selective diversification of their exposures. In this paper, we analyse how CCLs impact the prices that institutions pay for their trades during everyday trading. We study a high-quality data set from a large electronic trading platform in the foreign exchange spot market that allows institutions to apply CCLs. We find empirically that CCLs had little impact on the vast majority of trades in this data set. We also study the impact of CCLs using a new model of trading. By simulating our model with different underlying CCL networks, we highlight that CCLs can have a major impact in some situations.","PeriodicalId":35818,"journal":{"name":"Applied Mathematical Finance","volume":"1 1","pages":"520 - 548"},"PeriodicalIF":0.0,"publicationDate":"2017-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86540744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Utility maximization under risk constraints and incomplete information for a market with a change point 具有变化点的市场的风险约束和不完全信息下的效用最大化
Applied Mathematical Finance Pub Date : 2017-09-03 DOI: 10.1080/1350486X.2017.1409080
O. Janke
{"title":"Utility maximization under risk constraints and incomplete information for a market with a change point","authors":"O. Janke","doi":"10.1080/1350486X.2017.1409080","DOIUrl":"https://doi.org/10.1080/1350486X.2017.1409080","url":null,"abstract":"ABSTRACT In this article, we consider an optimization problem of expected utility maximization of continuous-time trading in a financial market. This trading is constrained by a benchmark for a utility-based shortfall risk measure. The market consists of one asset whose price process is modelled by a Geometric Brownian motion where the market parameters change at a random time. The information flow is modelled by initially and progressively enlarged filtrations which represent the knowledge about the price process, the Brownian motion and the random time. We solve the maximization problem and give the optimal terminal wealth depending on these different filtrations for general utility functions by using martingale representation results for the corresponding filtration.","PeriodicalId":35818,"journal":{"name":"Applied Mathematical Finance","volume":"58 1","pages":"451 - 484"},"PeriodicalIF":0.0,"publicationDate":"2017-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85644501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimal portfolio execution under time-varying liquidity constraints 时变流动性约束下的最优投资组合执行
Applied Mathematical Finance Pub Date : 2017-09-03 DOI: 10.1080/1350486X.2017.1405731
Hualing Lin, Arash Fahim
{"title":"Optimal portfolio execution under time-varying liquidity constraints","authors":"Hualing Lin, Arash Fahim","doi":"10.1080/1350486X.2017.1405731","DOIUrl":"https://doi.org/10.1080/1350486X.2017.1405731","url":null,"abstract":"ABSTRACT In this article, we take an algorithmic approach to solve the problem of optimal execution under time-varying constraints on the depth of a limit order book (LOB). Our algorithms are within the resilience model proposed by Obizhaeva and Wang (2013) with a more realistic assumption on the order book depth; the amount of liquidity provided by an LOB market is finite at all times. For the simplest case where the order book depth stays at a fixed level for the entire trading horizon, we reduce the optimal execution problem into a one-dimensional root-finding problem which can be readily solved by standard numerical algorithms. When the depth of the order book is monotone in time, we apply the Karush-Kuhn-Tucker conditions to narrow down the set of candidate strategies. Then, we use a dichotomy-based search algorithm to pin down the optimal one. For the general case, we start from the optimal strategy subject to no liquidity constraints and iterate over execution strategy by sequentially adding more constraints to the problem in a specific fashion until primal feasibility is achieved. Numerical experiments indicate that our algorithms give comparable results to those of current existing convex optimization toolbox CVXOPT with significantly lower time complexity.","PeriodicalId":35818,"journal":{"name":"Applied Mathematical Finance","volume":"112 1","pages":"387 - 416"},"PeriodicalIF":0.0,"publicationDate":"2017-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78146959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Extended Gini-Type Measures of Risk and Variability 扩展基尼型风险和变异性测量
Applied Mathematical Finance Pub Date : 2017-07-23 DOI: 10.2139/ssrn.3007948
Mohammed Berkhouch, G. Lakhnati, M. Righi
{"title":"Extended Gini-Type Measures of Risk and Variability","authors":"Mohammed Berkhouch, G. Lakhnati, M. Righi","doi":"10.2139/ssrn.3007948","DOIUrl":"https://doi.org/10.2139/ssrn.3007948","url":null,"abstract":"ABSTRACT The aim of this paper is to introduce a risk measure, Extended Gini Shortfall (EGS), that extends the Gini-type measures of risk and variability by taking risk aversion into consideration. Our risk measure is coherent and catches variability, an important concept for risk management. The analysis is made under the Choquet integral representations framework. We expose results for analytic computation under well-known distribution functions. Furthermore, we provide a practical application.","PeriodicalId":35818,"journal":{"name":"Applied Mathematical Finance","volume":"14 1","pages":"295 - 314"},"PeriodicalIF":0.0,"publicationDate":"2017-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83317406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 14
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