In this paper,we study the valuation of vulnerable European options incorporating the reduced-form approach,which models the credit default of the counterparty.We provide an analytical pricing model in which the compo...In this paper,we study the valuation of vulnerable European options incorporating the reduced-form approach,which models the credit default of the counterparty.We provide an analytical pricing model in which the components of the state processes,including the dynamics of the underlying asset value and the intensity process corresponding to the default event,are cross-exciting and they could facilitate the description of complex structure of events dependence.To illustrate how our model works,we present an application when the state variables follow specific affine jump-diffusion processes.Semi-analytical pricing formulae are obtained through a system of matrix Riccati equations.The derived formula can be implemented numerically,and we give numerical analysis to investigate the impact of the dynamic correlation between jump risk of the underlying asset value and default risk of the counterparty.展开更多
In this study, loss estimation models were developed for reasonably accurate assessment of economic and human losses from seismic events in the Mediterranean region, based on damage assessment at an urban scale.Data w...In this study, loss estimation models were developed for reasonably accurate assessment of economic and human losses from seismic events in the Mediterranean region, based on damage assessment at an urban scale.Data were compiled from existing worldwide databases,and completed with earthquake information from regional studies. Economic data were converted to a single common currency unit(2015 USD value) and the wealth of the areas affected by 65 earthquakes of the region from 1900 to 2015 was assessed. Reduced-form models were used to determine economic and human losses, with earthquake magnitude and intensity as hazard-related variables, and gross domestic product of the affected area and the affected population as exposure-related variables. Damage to buildings was also used as a hazard-related variable to predict economic and human losses. Finally, site-specific regression models were proposed for economic and human losses due to earthquakes in the Mediterranean region, and more specifically, in Algeria. We show that by introducing the damage variable into the models, prediction error can be reduced, and that accuracy of loss model estimation is site dependent and requires regional data on earthquake losses to improve. A case study for Constantine, Algeria shows the improvements needed for increased accuracy.展开更多
Based on the reduced-form approach, this paper investigates the pricing problems of default-risk bonds and credit default swaps(CDSs) for a fractional stochastic interest rate model with jump under the framework of pr...Based on the reduced-form approach, this paper investigates the pricing problems of default-risk bonds and credit default swaps(CDSs) for a fractional stochastic interest rate model with jump under the framework of primary-secondary. Using properties of the quasi-martingale with respect to the fractional Brownian motion and the jump technique in Park(2008), the authors first derive the explicit pricing formula of defaultable bonds. Then, based on the newly obtained pricing formula of defaultable bonds, the CDS is priced by the arbitrage-free principle. This paper presents an extension of the primary-secondary framework in Jarrow and Yu(2001).展开更多
文章探讨了轧差在对含有交易对手风险的衍生品定价时的影响.这里的研究对象是期权的多空组合,从交易双方违约独立假设到违约相关假设,采用约化的方法推导了组合价值在考虑了轧差和不考虑轧差时满足的偏微分方程,并且分别计算了两种假设...文章探讨了轧差在对含有交易对手风险的衍生品定价时的影响.这里的研究对象是期权的多空组合,从交易双方违约独立假设到违约相关假设,采用约化的方法推导了组合价值在考虑了轧差和不考虑轧差时满足的偏微分方程,并且分别计算了两种假设下轧差对于投资组合的影响.我们发现考虑轧差之后,组合的CVA(credit Value Adjustment)小于不考虑轧差时的CVA值,也就是说,轧差可以很大程度地降低违约后的损失.展开更多
In this paper we extend the reduced-form setting under model uncertainty introduced in[5]to include intensities following an affine process under parameter uncertainty,as defined in[15].This framework allows us to int...In this paper we extend the reduced-form setting under model uncertainty introduced in[5]to include intensities following an affine process under parameter uncertainty,as defined in[15].This framework allows us to introduce a longevity bond under model uncertainty in a way consistent with the classical case under one prior and to compute its valuation numerically.Moreover,we price a contingent claim with the sublinear conditional operator such that the extended market is still arbitrage-free in the sense of“no arbitrage of the first kind”as in[6].展开更多
基金The work of Huawei Niu in this paper was supported by National Natural Science Foundation of China(71871120,71501099)Key Project of Philosophy and Social Science Research in Universities in Jiangsu Province(2018SJZDI101)+2 种基金Six Talent Peaks Project in Jiangsu Province(SZCY-012)and Qing Lan Project in Jiangsu ProvinceThe work of Yu Xing was supported by Natural Science Foundation for Youths of Jiangsu of China(BK20171072).
文摘In this paper,we study the valuation of vulnerable European options incorporating the reduced-form approach,which models the credit default of the counterparty.We provide an analytical pricing model in which the components of the state processes,including the dynamics of the underlying asset value and the intensity process corresponding to the default event,are cross-exciting and they could facilitate the description of complex structure of events dependence.To illustrate how our model works,we present an application when the state variables follow specific affine jump-diffusion processes.Semi-analytical pricing formulae are obtained through a system of matrix Riccati equations.The derived formula can be implemented numerically,and we give numerical analysis to investigate the impact of the dynamic correlation between jump risk of the underlying asset value and default risk of the counterparty.
基金The MAIF Foundationsponsored by the Urban Seismology project at the Institute of Earth Science ISTerre of the University of Grenoble-Alpes Observatoire des Sciences de Univers de Grenoble (The Grenoble Observatory for Sciences of the Universe-Labex OSUG@2020) (Investissements d’avenir, ANR10LABX56)
文摘In this study, loss estimation models were developed for reasonably accurate assessment of economic and human losses from seismic events in the Mediterranean region, based on damage assessment at an urban scale.Data were compiled from existing worldwide databases,and completed with earthquake information from regional studies. Economic data were converted to a single common currency unit(2015 USD value) and the wealth of the areas affected by 65 earthquakes of the region from 1900 to 2015 was assessed. Reduced-form models were used to determine economic and human losses, with earthquake magnitude and intensity as hazard-related variables, and gross domestic product of the affected area and the affected population as exposure-related variables. Damage to buildings was also used as a hazard-related variable to predict economic and human losses. Finally, site-specific regression models were proposed for economic and human losses due to earthquakes in the Mediterranean region, and more specifically, in Algeria. We show that by introducing the damage variable into the models, prediction error can be reduced, and that accuracy of loss model estimation is site dependent and requires regional data on earthquake losses to improve. A case study for Constantine, Algeria shows the improvements needed for increased accuracy.
基金supported by the National Natural Science Foundation of China under Grant Nos.11401556,61304065 and 11471304the Fundamental Research Funds for the Central Universities under Grant No.WK2040000012
文摘Based on the reduced-form approach, this paper investigates the pricing problems of default-risk bonds and credit default swaps(CDSs) for a fractional stochastic interest rate model with jump under the framework of primary-secondary. Using properties of the quasi-martingale with respect to the fractional Brownian motion and the jump technique in Park(2008), the authors first derive the explicit pricing formula of defaultable bonds. Then, based on the newly obtained pricing formula of defaultable bonds, the CDS is priced by the arbitrage-free principle. This paper presents an extension of the primary-secondary framework in Jarrow and Yu(2001).
文摘文章探讨了轧差在对含有交易对手风险的衍生品定价时的影响.这里的研究对象是期权的多空组合,从交易双方违约独立假设到违约相关假设,采用约化的方法推导了组合价值在考虑了轧差和不考虑轧差时满足的偏微分方程,并且分别计算了两种假设下轧差对于投资组合的影响.我们发现考虑轧差之后,组合的CVA(credit Value Adjustment)小于不考虑轧差时的CVA值,也就是说,轧差可以很大程度地降低违约后的损失.
文摘In this paper we extend the reduced-form setting under model uncertainty introduced in[5]to include intensities following an affine process under parameter uncertainty,as defined in[15].This framework allows us to introduce a longevity bond under model uncertainty in a way consistent with the classical case under one prior and to compute its valuation numerically.Moreover,we price a contingent claim with the sublinear conditional operator such that the extended market is still arbitrage-free in the sense of“no arbitrage of the first kind”as in[6].
