This paper presents structural approach for the valuation of credit risk. Credit risk arises whenever a borrower is expecting to use future cash flows to pay a current debt. It is closely tied to the potential return ...This paper presents structural approach for the valuation of credit risk. Credit risk arises whenever a borrower is expecting to use future cash flows to pay a current debt. It is closely tied to the potential return of investment, the most notable being that the yields on bonds correlate strongly to their perceived credit risk. Structural approach is based on the volatility of the total value of the firm. The credit risk to this measured in a standard way. The random time of default is defined in an intuition way. The default event is linked to the notion of the firm＇s insolvency. This approach is known to generated low credit spreads for corporate bonds close to maturity. It requires a judicious specification of the default barrier in order to get a good fit to the observed spread curves.展开更多
Classical indifference valuation,a widely studied approach in incomplete markets,uses critically the a priori knowledge of the characteristics(arrival,maturity,payoff structure)of the projects in consideration.This as...Classical indifference valuation,a widely studied approach in incomplete markets,uses critically the a priori knowledge of the characteristics(arrival,maturity,payoff structure)of the projects in consideration.This assumption,however,may not accommodate realistic scenarios in which projects,not initially anticipated,arrive at later times.To accommodate this,we employ forward indifference valuation criteria,which by construction are flexible enough to adapt to such"non-anticipated"cases while yielding time-consistent indifference prices.We consider and analyze in detail two representative cases:valuation adjustments due to incoming non-anticipated project and the relative forward indifference valuation of new projects in relation to existing ones.展开更多
This paper presents a new approach for offshore risk analysis that is capable of dealing with linguistic probabilities in Bayesian networks （ BNs）. In this paper, linguistic probabilities are used to describe occurr...This paper presents a new approach for offshore risk analysis that is capable of dealing with linguistic probabilities in Bayesian networks （ BNs）. In this paper, linguistic probabilities are used to describe occurrence likelihood of hazardous events that may cause possible accidents in offshore operations. In order to use fuzzy information, an f-weighted valuation function is proposed to transform linguistic judgements into crisp probability distributions which can be easily put into a BN to model causal relationships among risk factors. The use of linguistic variables makes it easier for human experts to express their knowledge, and the transformation of linguistic judgements into crisp probabilities can significantly save the cost of computation, modifying and maintaining a BN model. The flexibility of the method allows for multiple forms of information to be used to quantify model relationships, including formally assessed expert opinion when quantitative data are lacking, or when only qualitative or vague statements can be made. The model is a modular representation of uncertain knowledge caused due to randomness, vagueness and ignorance. This makes the risk analysis of offshore engineering systems more functional and easier in many assessment contexts. Specifically, the proposed f-weighted valuation function takes into account not only the dominating values, but also the a-level values that are ignored by conventional valuation methods. A case study of the collision risk between a Floating Production, Storage and Off-loading （FPSO） unit and the anthorised vessels due to human elements during operation is used to illustrate the application of the proposed model.展开更多
The authors employ the recent stochastic-control-based approach to financial mathematicsto solve a problem of determination of the risk premium for a stochastic interest rate model,andthe corresponding problem of equi...The authors employ the recent stochastic-control-based approach to financial mathematicsto solve a problem of determination of the risk premium for a stochastic interest rate model,andthe corresponding problem of equity valuation.The risk premium is determined explicitly,by meansof solving a corresponding partial differential equation (PDE),in two forms:one,time-dependent,corresponding to a finite time contract expiration,and the simpler version corresponding to perpetualcontracts.As stocks are perpetual contracts,when solving the problem of equity valuation,the latterform of the risk premium is used.By means of solving the general pricing PDE,an efficient equityvaluation method was developed that is a combination of some sophisticated explicit formulas,and anumerical procedure.展开更多
The t-distribution has a “fat tail” feature, which is more suitable than the normal probability density function to describe the distribution characteristics of return on assets. The difficulty of using t-distributi...The t-distribution has a “fat tail” feature, which is more suitable than the normal probability density function to describe the distribution characteristics of return on assets. The difficulty of using t-distribution to price European options is that a fat tail can lead to a deviation in one integral required for option pricing. We use a distribution called logarithmic truncated t-distribution to price European options. A risk neutral valuation method was used to obtain a European option pricing model with logarithmic truncated t-distribution.展开更多
文摘This paper presents structural approach for the valuation of credit risk. Credit risk arises whenever a borrower is expecting to use future cash flows to pay a current debt. It is closely tied to the potential return of investment, the most notable being that the yields on bonds correlate strongly to their perceived credit risk. Structural approach is based on the volatility of the total value of the firm. The credit risk to this measured in a standard way. The random time of default is defined in an intuition way. The default event is linked to the notion of the firm＇s insolvency. This approach is known to generated low credit spreads for corporate bonds close to maturity. It requires a judicious specification of the default barrier in order to get a good fit to the observed spread curves.
文摘Classical indifference valuation,a widely studied approach in incomplete markets,uses critically the a priori knowledge of the characteristics(arrival,maturity,payoff structure)of the projects in consideration.This assumption,however,may not accommodate realistic scenarios in which projects,not initially anticipated,arrive at later times.To accommodate this,we employ forward indifference valuation criteria,which by construction are flexible enough to adapt to such"non-anticipated"cases while yielding time-consistent indifference prices.We consider and analyze in detail two representative cases:valuation adjustments due to incoming non-anticipated project and the relative forward indifference valuation of new projects in relation to existing ones.
基金This project is funded bythe UK Engineering and Physical Sciences Research Council (EPSRC) under Grant Refer-ences:GR/S85504 and GR/S85498
文摘This paper presents a new approach for offshore risk analysis that is capable of dealing with linguistic probabilities in Bayesian networks （ BNs）. In this paper, linguistic probabilities are used to describe occurrence likelihood of hazardous events that may cause possible accidents in offshore operations. In order to use fuzzy information, an f-weighted valuation function is proposed to transform linguistic judgements into crisp probability distributions which can be easily put into a BN to model causal relationships among risk factors. The use of linguistic variables makes it easier for human experts to express their knowledge, and the transformation of linguistic judgements into crisp probabilities can significantly save the cost of computation, modifying and maintaining a BN model. The flexibility of the method allows for multiple forms of information to be used to quantify model relationships, including formally assessed expert opinion when quantitative data are lacking, or when only qualitative or vague statements can be made. The model is a modular representation of uncertain knowledge caused due to randomness, vagueness and ignorance. This makes the risk analysis of offshore engineering systems more functional and easier in many assessment contexts. Specifically, the proposed f-weighted valuation function takes into account not only the dominating values, but also the a-level values that are ignored by conventional valuation methods. A case study of the collision risk between a Floating Production, Storage and Off-loading （FPSO） unit and the anthorised vessels due to human elements during operation is used to illustrate the application of the proposed model.
基金supported in part by the Center for Financial Engineering at the Suzhou University, Chinathe Taft Research Center at the University of Cincinnati, USA
文摘The authors employ the recent stochastic-control-based approach to financial mathematicsto solve a problem of determination of the risk premium for a stochastic interest rate model,andthe corresponding problem of equity valuation.The risk premium is determined explicitly,by meansof solving a corresponding partial differential equation (PDE),in two forms:one,time-dependent,corresponding to a finite time contract expiration,and the simpler version corresponding to perpetualcontracts.As stocks are perpetual contracts,when solving the problem of equity valuation,the latterform of the risk premium is used.By means of solving the general pricing PDE,an efficient equityvaluation method was developed that is a combination of some sophisticated explicit formulas,and anumerical procedure.
文摘The t-distribution has a “fat tail” feature, which is more suitable than the normal probability density function to describe the distribution characteristics of return on assets. The difficulty of using t-distribution to price European options is that a fat tail can lead to a deviation in one integral required for option pricing. We use a distribution called logarithmic truncated t-distribution to price European options. A risk neutral valuation method was used to obtain a European option pricing model with logarithmic truncated t-distribution.
