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
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 considers utility indifference valuation of derivatives under model uncertainty and trading constraints, where the utility is formulated as an additive stochastic differential utility of both intertemporal ...This paper considers utility indifference valuation of derivatives under model uncertainty and trading constraints, where the utility is formulated as an additive stochastic differential utility of both intertemporal consumption and terminal wealth, and the uncertain prospects are ranked according to a multiple-priors model of Chen and Epstein(2002). The price is determined by two optimal stochastic control problems(mixed with optimal stopping time in the case of American option) of forward-backward stochastic differential equations.By means of backward stochastic differential equation and partial differential equation methods, we show that both bid and ask prices are closely related to the Black-Scholes risk-neutral price with modified dividend rates.The two prices will actually coincide with each other if there is no trading constraint or the model uncertainty disappears. Finally, two applications to European option and American option are discussed.展开更多
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.
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supported by National Natural Science Foundation of China(Grant Nos.11271143,11371155 and 11326199)University Special Research Fund for Ph D Program(Grant No.20124407110001)+1 种基金National Natural Science Foundation of Zhejiang Province(Grant No.Y6110775)the Oxford-Man Institute of Quantitative Finance
文摘This paper considers utility indifference valuation of derivatives under model uncertainty and trading constraints, where the utility is formulated as an additive stochastic differential utility of both intertemporal consumption and terminal wealth, and the uncertain prospects are ranked according to a multiple-priors model of Chen and Epstein(2002). The price is determined by two optimal stochastic control problems(mixed with optimal stopping time in the case of American option) of forward-backward stochastic differential equations.By means of backward stochastic differential equation and partial differential equation methods, we show that both bid and ask prices are closely related to the Black-Scholes risk-neutral price with modified dividend rates.The two prices will actually coincide with each other if there is no trading constraint or the model uncertainty disappears. Finally, two applications to European option and American option are discussed.
