We will study the following problem.Let X_t,t∈[0,T],be an R^d-valued process defined on atime interval t∈[0,T].Let Y be a random value depending on the trajectory of X.Assume that,at each fixedtime t≤T,the informat...We will study the following problem.Let X_t,t∈[0,T],be an R^d-valued process defined on atime interval t∈[0,T].Let Y be a random value depending on the trajectory of X.Assume that,at each fixedtime t≤T,the information available to an agent(an individual,a firm,or even a market)is the trajectory ofX before t.Thus at time T,the random value of Y(ω) will become known to this agent.The question is:howwill this agent evaluate Y at the time t?We will introduce an evaluation operator ε_t[Y] to define the value of Y given by this agent at time t.Thisoperator ε_t[·] assigns an (X_s)0(?)s(?)T-dependent random variable Y to an (X_s)0(?)s(?)t-dependent random variableε_t[Y].We will mainly treat the situation in which the process X is a solution of a SDE (see equation (3.1)) withthe drift coefficient b and diffusion coefficient σ containing an unknown parameter θ=θ_t.We then consider theso called super evaluation when the agent is a seller of the asset Y.We will prove that such super evaluation is afiltration consistent nonlinear expectation.In some typical situations,we will prove that a filtration consistentnonlinear evaluation dominated by this super evaluation is a g-evaluation.We also consider the correspondingnonlinear Markovian situation.展开更多
In this paper,we consider the price of catastrophe options with credit risk in a regime-switching model.We assume that the macroeconomic states are described by a continuous-time Markov chain with a finite state space...In this paper,we consider the price of catastrophe options with credit risk in a regime-switching model.We assume that the macroeconomic states are described by a continuous-time Markov chain with a finite state space.By using the measure change technique,we derive the price expressions of catastrophe put options.Moreover,we conduct some numerical analysis to demonstrate how the parameters of the model affect the price of the catastrophe put option.展开更多
The problems of online pricing with offline data,among other similar online decision making with offline data problems,aim at designing and evaluating online pricing policies in presence of a certain amount of existin...The problems of online pricing with offline data,among other similar online decision making with offline data problems,aim at designing and evaluating online pricing policies in presence of a certain amount of existing offline data.To evaluate pricing policies when offline data are available,the decision maker can either position herself at the time point when the offline data are already observed and viewed as deterministic,or at the time point when the offline data are not yet generated and viewed as stochastic.We write a framework to discuss how and why these two different positions are relevant to online policy evaluations,from a worst-case perspective and from a Bayesian perspective.We then use a simple online pricing setting with offline data to illustrate the constructions of optimal policies for these two approaches and discuss their differences,especially whether we can decompose the searching for the optimal policy into independent subproblems and optimize separately,and whether there exists a deterministic optimal policy.展开更多
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
Binomial no-arbitrage price have a method is the traditional approach for derivative pricing,which is,the complete model,which makes possible the perfect replication in the market.Risk neutral pricing is an appropriat...Binomial no-arbitrage price have a method is the traditional approach for derivative pricing,which is,the complete model,which makes possible the perfect replication in the market.Risk neutral pricing is an appropriate method of asset pricing in a complete market.We have discussed an incomplete market,a non-transaction asset that produces incompleteness of the market.An effective method of asset pricing in incomplete markets is the undifferentiated pricing method.This technique was firstly introduced by Bernoulli in(1738)the sense of gambling,lottery and their expected return.It is used to command investors'preferences and better returns the results they expect.In addition,we also discuss the utility function,which is the core element of the undifferentiated pricing.We also studied some important behavior preferences of agents,and injected exponential effect of risk aversion in the model,so that the model was nonlinear in the process of claim settlement.展开更多
In the context of model uncertainty, we study the optimal design and the pricing of financial instruments aiming to hedge some of non-tradable risks. For the existence of model uncertainty, the preference can be repre...In the context of model uncertainty, we study the optimal design and the pricing of financial instruments aiming to hedge some of non-tradable risks. For the existence of model uncertainty, the preference can be represented by the robust expected utility （also called maxmin expected utility） which can be put in the framework of sublinear expectation. The problem of maximizing the issuer＇s robust expected utility under the constraint imposed by the buyer can be transformed to the problem of minimizing the issuer＇s convex measure under the corresponding constraint. And here the convex measure measures not only the risks but also the model uncertainties.展开更多
In this study,we aim at developing a model for option pricing to reduce the risks associated with Ethiopian coffee price fluctuations.We used daily closed Washed Sidama class A Grade3(WSDA3)coffee price recorded in th...In this study,we aim at developing a model for option pricing to reduce the risks associated with Ethiopian coffee price fluctuations.We used daily closed Washed Sidama class A Grade3(WSDA3)coffee price recorded in the period 31 May 2011 to 30 March 2018 obtained from Ethiopia commodity exchange(ECX)market to analyse the price fluctuation.The nature of log-returns of the price is asymmetric(negatively skewed)and exhibits high kurtosis.We used jump diffusion models for modeling and option pricing the coffee price.The method of maximum likelihood is applied to estimate the parameters of the models.We used the root mean square error(RMSE)to test the validation of the models.The values of RMSE for Merton’s and double exponential jump diffusion models are 0.1093 and 0.0783,respectively.These results indicate that the models fit the data very well.We used analytical and Monte Carlo technique to find the call option pricing of WSDA3 price.Based on the empirical results,we concluded that double exponential jump diffusion model is more efficient than Merton’s model for modeling and option pricing of this coffee price.展开更多
基金Supported in part by National Natural Science Foundation of China Grant (No.10131040).The author also thanks the referee's constructive suggestions.
文摘We will study the following problem.Let X_t,t∈[0,T],be an R^d-valued process defined on atime interval t∈[0,T].Let Y be a random value depending on the trajectory of X.Assume that,at each fixedtime t≤T,the information available to an agent(an individual,a firm,or even a market)is the trajectory ofX before t.Thus at time T,the random value of Y(ω) will become known to this agent.The question is:howwill this agent evaluate Y at the time t?We will introduce an evaluation operator ε_t[Y] to define the value of Y given by this agent at time t.Thisoperator ε_t[·] assigns an (X_s)0(?)s(?)T-dependent random variable Y to an (X_s)0(?)s(?)t-dependent random variableε_t[Y].We will mainly treat the situation in which the process X is a solution of a SDE (see equation (3.1)) withthe drift coefficient b and diffusion coefficient σ containing an unknown parameter θ=θ_t.We then consider theso called super evaluation when the agent is a seller of the asset Y.We will prove that such super evaluation is afiltration consistent nonlinear expectation.In some typical situations,we will prove that a filtration consistentnonlinear evaluation dominated by this super evaluation is a g-evaluation.We also consider the correspondingnonlinear Markovian situation.
基金supported by the Jiangsu University Philosophy and Social Science Research Project(Grant No.2019SJA1326).
文摘In this paper,we consider the price of catastrophe options with credit risk in a regime-switching model.We assume that the macroeconomic states are described by a continuous-time Markov chain with a finite state space.By using the measure change technique,we derive the price expressions of catastrophe put options.Moreover,we conduct some numerical analysis to demonstrate how the parameters of the model affect the price of the catastrophe put option.
文摘The problems of online pricing with offline data,among other similar online decision making with offline data problems,aim at designing and evaluating online pricing policies in presence of a certain amount of existing offline data.To evaluate pricing policies when offline data are available,the decision maker can either position herself at the time point when the offline data are already observed and viewed as deterministic,or at the time point when the offline data are not yet generated and viewed as stochastic.We write a framework to discuss how and why these two different positions are relevant to online policy evaluations,from a worst-case perspective and from a Bayesian perspective.We then use a simple online pricing setting with offline data to illustrate the constructions of optimal policies for these two approaches and discuss their differences,especially whether we can decompose the searching for the optimal policy into independent subproblems and optimize separately,and whether there exists a deterministic optimal policy.
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.
文摘Binomial no-arbitrage price have a method is the traditional approach for derivative pricing,which is,the complete model,which makes possible the perfect replication in the market.Risk neutral pricing is an appropriate method of asset pricing in a complete market.We have discussed an incomplete market,a non-transaction asset that produces incompleteness of the market.An effective method of asset pricing in incomplete markets is the undifferentiated pricing method.This technique was firstly introduced by Bernoulli in(1738)the sense of gambling,lottery and their expected return.It is used to command investors'preferences and better returns the results they expect.In addition,we also discuss the utility function,which is the core element of the undifferentiated pricing.We also studied some important behavior preferences of agents,and injected exponential effect of risk aversion in the model,so that the model was nonlinear in the process of claim settlement.
基金Supported by Beijing Natural Science Foundation(Grant No.1112009)
文摘In the context of model uncertainty, we study the optimal design and the pricing of financial instruments aiming to hedge some of non-tradable risks. For the existence of model uncertainty, the preference can be represented by the robust expected utility （also called maxmin expected utility） which can be put in the framework of sublinear expectation. The problem of maximizing the issuer＇s robust expected utility under the constraint imposed by the buyer can be transformed to the problem of minimizing the issuer＇s convex measure under the corresponding constraint. And here the convex measure measures not only the risks but also the model uncertainties.
文摘In this study,we aim at developing a model for option pricing to reduce the risks associated with Ethiopian coffee price fluctuations.We used daily closed Washed Sidama class A Grade3(WSDA3)coffee price recorded in the period 31 May 2011 to 30 March 2018 obtained from Ethiopia commodity exchange(ECX)market to analyse the price fluctuation.The nature of log-returns of the price is asymmetric(negatively skewed)and exhibits high kurtosis.We used jump diffusion models for modeling and option pricing the coffee price.The method of maximum likelihood is applied to estimate the parameters of the models.We used the root mean square error(RMSE)to test the validation of the models.The values of RMSE for Merton’s and double exponential jump diffusion models are 0.1093 and 0.0783,respectively.These results indicate that the models fit the data very well.We used analytical and Monte Carlo technique to find the call option pricing of WSDA3 price.Based on the empirical results,we concluded that double exponential jump diffusion model is more efficient than Merton’s model for modeling and option pricing of this coffee price.
