In this paper, we study the price of catastrophe Options with counterparty credit risk in a reduced form model. We assume that the loss process is generated by a doubly stochastic Poisson process, the share price proc...In this paper, we study the price of catastrophe Options with counterparty credit risk in a reduced form model. We assume that the loss process is generated by a doubly stochastic Poisson process, the share price process is modeled through a jump-diffusion process which is correlated to the loss process, the interest rate process and the default intensity process are modeled through the Vasicek model： We derive the closed form formulae for pricing catastrophe options in a reduced form model. Furthermore, we make some numerical analysis on the explicit formulae.展开更多
Designing effective control policy requires accurate quantification of the relationship between the ambient concentrations of O3and PM2.5and the emissions of their precursors.However,the challenge is that precursor re...Designing effective control policy requires accurate quantification of the relationship between the ambient concentrations of O3and PM2.5and the emissions of their precursors.However,the challenge is that precursor reduction does not necessarily lead to decreases in the concentrations of O3and PM2.5,which are formed by multiple precursors under complex physical and chemical processes;this calls for the development of advanced model technologies to provide accurate predictions of the nonlinear responses of air quality to emissions.Different from the traditional sensitivity analysis and source apportionment methods,the reduced form models(RFMs)based on chemical transport models(CTMs)are able to quantify air quality responses to emissions more accurately and efficiently with lower computational cost.Here we review recent approaches used in RFMs and compare their structures,advantages and disadvantages,performance and applications.In general,RFMs are classified into three types including(1)sensitivity-based models,(2)models with simplified chemistry and physical processes,and(3)statistical models,with considerable differences in principles,characteristics and application ranges.The prediction of nonlinear responses by RFMs enables more in-depth analysis,not only in terms of real-time prediction of concentrations and quantification of human exposure,health impacts and economic damage,but also in optimizing control policies.Notably,data assimilation and emission inventory inversion based on the nonlinear response of concentrations to emissions can also be greatly beneficial to air pollution control management.In future studies,improvement in the performance of CTMs is exceedingly crucial to obtain a more reliable baseline for the prediction of air quality responses.Development of models to determine the air quality response to emissions under varying meteorological conditions is also necessary in the context of future climate changes,which pose great challenges to the quantification of response relationships.Additionally,with rising requirements for fine-scale air quality management,improving the performance of urban-scale simulations is worth considering.In short,accurate predictions of the response of air quality to emissions,though challenging,holds great promise for the present as well as for future scenarios.展开更多
In this paper we analyze the main characteristics of correlative clients and the revolver loan and reduced form models for the correlative clients A and B in real-life. This is done by decomposing the default intensit...In this paper we analyze the main characteristics of correlative clients and the revolver loan and reduced form models for the correlative clients A and B in real-life. This is done by decomposing the default intensity into specific default intensity and homogenous default intensity. We also use a mathematical formula of the default joint distribution function and the marginal distribution function in the physical measure to deduce the martingale measure. The modeling idea on pricing the revolver loan with client A is presented by applying reduced form model. Through calculating the cost and income fund flows under the martingale measure, the framework of a “break-even” pricing model is established. The conclusion is that the interest rate of a revolver loan for client A on the “break-even” point is not related to the maximum authorized amount and the drawdown amount at that time under some assumptions, but only rests with credit rating and homogenous default intensity of client A and B as well as loan term of client A.展开更多
基金supported by the National Natural Science Foundation of China(11371274)
文摘In this paper, we study the price of catastrophe Options with counterparty credit risk in a reduced form model. We assume that the loss process is generated by a doubly stochastic Poisson process, the share price process is modeled through a jump-diffusion process which is correlated to the loss process, the interest rate process and the default intensity process are modeled through the Vasicek model： We derive the closed form formulae for pricing catastrophe options in a reduced form model. Furthermore, we make some numerical analysis on the explicit formulae.
基金supported by the National Key R&D program of China(Nos.2019YFC0214800 and 2018YFC0213805)the National Natural Science Foundation of China(No.41907190)Shanghai Science and Technology Commission Scientific Research Project(No.19DZ1205006)。
文摘Designing effective control policy requires accurate quantification of the relationship between the ambient concentrations of O3and PM2.5and the emissions of their precursors.However,the challenge is that precursor reduction does not necessarily lead to decreases in the concentrations of O3and PM2.5,which are formed by multiple precursors under complex physical and chemical processes;this calls for the development of advanced model technologies to provide accurate predictions of the nonlinear responses of air quality to emissions.Different from the traditional sensitivity analysis and source apportionment methods,the reduced form models(RFMs)based on chemical transport models(CTMs)are able to quantify air quality responses to emissions more accurately and efficiently with lower computational cost.Here we review recent approaches used in RFMs and compare their structures,advantages and disadvantages,performance and applications.In general,RFMs are classified into three types including(1)sensitivity-based models,(2)models with simplified chemistry and physical processes,and(3)statistical models,with considerable differences in principles,characteristics and application ranges.The prediction of nonlinear responses by RFMs enables more in-depth analysis,not only in terms of real-time prediction of concentrations and quantification of human exposure,health impacts and economic damage,but also in optimizing control policies.Notably,data assimilation and emission inventory inversion based on the nonlinear response of concentrations to emissions can also be greatly beneficial to air pollution control management.In future studies,improvement in the performance of CTMs is exceedingly crucial to obtain a more reliable baseline for the prediction of air quality responses.Development of models to determine the air quality response to emissions under varying meteorological conditions is also necessary in the context of future climate changes,which pose great challenges to the quantification of response relationships.Additionally,with rising requirements for fine-scale air quality management,improving the performance of urban-scale simulations is worth considering.In short,accurate predictions of the response of air quality to emissions,though challenging,holds great promise for the present as well as for future scenarios.
文摘In this paper we analyze the main characteristics of correlative clients and the revolver loan and reduced form models for the correlative clients A and B in real-life. This is done by decomposing the default intensity into specific default intensity and homogenous default intensity. We also use a mathematical formula of the default joint distribution function and the marginal distribution function in the physical measure to deduce the martingale measure. The modeling idea on pricing the revolver loan with client A is presented by applying reduced form model. Through calculating the cost and income fund flows under the martingale measure, the framework of a “break-even” pricing model is established. The conclusion is that the interest rate of a revolver loan for client A on the “break-even” point is not related to the maximum authorized amount and the drawdown amount at that time under some assumptions, but only rests with credit rating and homogenous default intensity of client A and B as well as loan term of client A.
