A model of using binomial tree pricing formulae in a fuzzy market is proposed. In the fuzzy market, a price interval can be got according to the belief degree. The rule for the reasonability of the price interval is p...A model of using binomial tree pricing formulae in a fuzzy market is proposed. In the fuzzy market, a price interval can be got according to the belief degree. The rule for the reasonability of the price interval is proposed. The explicit expression of the interval is discussed in some special settings.展开更多
The method for pricing the option in a market with interval number factors is proposed. The no-arbitrage principle in the interval number valued market and the rule to judge the reasonability of a price interval are g...The method for pricing the option in a market with interval number factors is proposed. The no-arbitrage principle in the interval number valued market and the rule to judge the reasonability of a price interval are given. Using the method, the price interval where the riskless interest and the volatility under B-S setting is given. The price interval from binomial tree model when the key factors u, d, R are all interval numbers is also discussed.展开更多
This paper provides a difference-in-opinions equilibrium framework for pricing asset and option in a multi-period binomial economy with heterogeneous beliefs.Agents agree to disagree about their beliefs on the probabi...This paper provides a difference-in-opinions equilibrium framework for pricing asset and option in a multi-period binomial economy with heterogeneous beliefs.Agents agree to disagree about their beliefs on the probability and asset return in each state of nature.By constructing a consensus belief,we examine the impact of heterogeneous beliefs on market equilibrium.We show that agents'wealth shares are expected to remain the same under the consensus belief,although they are expected to increase under their own beliefs.Also large disagreement leads to lower risk premium,while high disagreement on the future return in up state(down state)leads to lower(higher)risk-free rate and expected return for the risky asset.Furthermore,under the consensus belief,the implied volatility of the call options exhibits some observed patterns widely documented in option markets.展开更多
The binomial tree method is the most popular numerical approach to pricing options. However,for currency lookback options,this method is not consistent with the corresponding continuous models,which leads to slow spee...The binomial tree method is the most popular numerical approach to pricing options. However,for currency lookback options,this method is not consistent with the corresponding continuous models,which leads to slow speed of convergence.On the basis of the PDE approach,we develop a consistent numerical scheme called the modified binomial tree method.It possesses one order of accuracy and its efficiency is demonstrated by numerical experiments.The convergence proofs are also produced in terms of numerical analysis and the notion of viscosity solution.展开更多
This paper presents simple and fast algorithms for computing very tight upper and lower bounds on the prices of American Asian options in the binomial model.The authors choose two types sets of the actual arithmetic a...This paper presents simple and fast algorithms for computing very tight upper and lower bounds on the prices of American Asian options in the binomial model.The authors choose two types sets of the actual arithmetic average prices,instead of the simulated values in other existing models,as the representative average prices at each node of the binomial tree.This approach simplifies effectively the computation and reduces the error caused by the linear interpolation.Numerical results show that the approach produces accurate upper and lower bounds compared to the other existing methods based on the binomial tree.展开更多
In this paper we use a binomial tree to price convertible bond with default risk. A new way about pricing convertible bonds is proposed, which belongs to the deduced form approach. Firstly an inhomogeneous Possion pro...In this paper we use a binomial tree to price convertible bond with default risk. A new way about pricing convertible bonds is proposed, which belongs to the deduced form approach. Firstly an inhomogeneous Possion process is used to describe default event and definition of default time. Secondly we combine the stock binomial tree with default intensity and obtain a new tree, then convertible bonds are priced according to the combined tree. It is worth pointing out that the model have following characters： simple, intuitive and having the strong ability to combine other items in convertible bonds＇ indenture.展开更多
文摘A model of using binomial tree pricing formulae in a fuzzy market is proposed. In the fuzzy market, a price interval can be got according to the belief degree. The rule for the reasonability of the price interval is proposed. The explicit expression of the interval is discussed in some special settings.
文摘The method for pricing the option in a market with interval number factors is proposed. The no-arbitrage principle in the interval number valued market and the rule to judge the reasonability of a price interval are given. Using the method, the price interval where the riskless interest and the volatility under B-S setting is given. The price interval from binomial tree model when the key factors u, d, R are all interval numbers is also discussed.
基金Financial support from the Australian Research Council(ARC)under Discovery Grant(DP130103210)the National Natural Science Foundation of China(NSFC)Grant(71320107003)。
文摘This paper provides a difference-in-opinions equilibrium framework for pricing asset and option in a multi-period binomial economy with heterogeneous beliefs.Agents agree to disagree about their beliefs on the probability and asset return in each state of nature.By constructing a consensus belief,we examine the impact of heterogeneous beliefs on market equilibrium.We show that agents'wealth shares are expected to remain the same under the consensus belief,although they are expected to increase under their own beliefs.Also large disagreement leads to lower risk premium,while high disagreement on the future return in up state(down state)leads to lower(higher)risk-free rate and expected return for the risky asset.Furthermore,under the consensus belief,the implied volatility of the call options exhibits some observed patterns widely documented in option markets.
基金Supported by National Science Foundation of China (No.19871062)
文摘The binomial tree method is the most popular numerical approach to pricing options. However,for currency lookback options,this method is not consistent with the corresponding continuous models,which leads to slow speed of convergence.On the basis of the PDE approach,we develop a consistent numerical scheme called the modified binomial tree method.It possesses one order of accuracy and its efficiency is demonstrated by numerical experiments.The convergence proofs are also produced in terms of numerical analysis and the notion of viscosity solution.
基金partially supported by China Postdoctoral Science Foundation under Grant No.2012M510377National Natural Science Foundation of China under Grant Nos.71373043,71331006,and 71171119+2 种基金the National Social Science Foundation of China under Grant No.11AZD010Program for New Century Excellent Talents in University under Grant No.NCET-10-0337Program for Excellent Talents,UIBE
文摘This paper presents simple and fast algorithms for computing very tight upper and lower bounds on the prices of American Asian options in the binomial model.The authors choose two types sets of the actual arithmetic average prices,instead of the simulated values in other existing models,as the representative average prices at each node of the binomial tree.This approach simplifies effectively the computation and reduces the error caused by the linear interpolation.Numerical results show that the approach produces accurate upper and lower bounds compared to the other existing methods based on the binomial tree.
基金This project is supported by National Natural Science Foundation of China （70440011） and Natural Science Found of Beijing （1052007）.
文摘In this paper we use a binomial tree to price convertible bond with default risk. A new way about pricing convertible bonds is proposed, which belongs to the deduced form approach. Firstly an inhomogeneous Possion process is used to describe default event and definition of default time. Secondly we combine the stock binomial tree with default intensity and obtain a new tree, then convertible bonds are priced according to the combined tree. It is worth pointing out that the model have following characters： simple, intuitive and having the strong ability to combine other items in convertible bonds＇ indenture.
