In this paper, the binomial tree method is introduced to price the European option under a class of jump-diffusion model. The purpose of the addressed problem is to find the parameters of the binomial tree and design ...In this paper, the binomial tree method is introduced to price the European option under a class of jump-diffusion model. The purpose of the addressed problem is to find the parameters of the binomial tree and design the pricing formula for European option. Compared with the continuous situation, the proposed value equation of option under the new binomial tree model converges to Merton’s accurate analytical solution, and the established binomial tree method can be proved to work better than the traditional binomial tree. Finally, a numerical example is presented to illustrate the effectiveness of the proposed pricing methods.展开更多
The interests of vulnerable groups can’t be guaranteed due to their weaker capacity and the limited interests demand channels during the water pollution conflicts. The interest protection for the vulnerable people in...The interests of vulnerable groups can’t be guaranteed due to their weaker capacity and the limited interests demand channels during the water pollution conflicts. The interest protection for the vulnerable people in the water pollution conflicts has attracted attentions of the international scholars. The paper tries to construct the market mechanism which can make the vulnerable people to involve in the emission trading. The vulnerable people can buy American put option in the emission trading market. When the price of the emission runs below the contract price, the vulnerable people can get the benefit through executing the option. When the price of the emission runs above the contract price, the vulnerable people can give up the right. The binomial tree option pricing model can help the vulnerable people to make a decision through the analysis of the worth of the American put option.展开更多
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
We present a parallel algorithm that computes the ask and bid prices of an American option when proportional transaction costs apply to trading in the underlying asset. The algorithm computes the prices on recombining...We present a parallel algorithm that computes the ask and bid prices of an American option when proportional transaction costs apply to trading in the underlying asset. The algorithm computes the prices on recombining binomial trees, and is designed for modern multi-core processors. Although parallel option pricing has been well studied, none of the existing approaches takes transaction costs into consideration. The algorithm that we propose partitions a binomial tree into blocks. In any round of computation a block is further partitioned into regions which are assigned to distinct processors. To minimise load imbalance the assignment of nodes to processors is dynamically adjusted before each new round starts. Synchronisation is required both within a round and between two successive rounds. The parallel speedup of the algorithm is proportional to the number of processors used. The parallel algorithm was implemented in C/C++ via POSIX Threads, and was tested on a machine with 8 processors. In the pricing of an American put option, the parallel speedup against an efficient sequential implementation was 5.26 using 8 processors and 1500 time steps, achieving a parallel efficiency of 65.75%.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 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
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
文摘In this paper, the binomial tree method is introduced to price the European option under a class of jump-diffusion model. The purpose of the addressed problem is to find the parameters of the binomial tree and design the pricing formula for European option. Compared with the continuous situation, the proposed value equation of option under the new binomial tree model converges to Merton’s accurate analytical solution, and the established binomial tree method can be proved to work better than the traditional binomial tree. Finally, a numerical example is presented to illustrate the effectiveness of the proposed pricing methods.
文摘The interests of vulnerable groups can’t be guaranteed due to their weaker capacity and the limited interests demand channels during the water pollution conflicts. The interest protection for the vulnerable people in the water pollution conflicts has attracted attentions of the international scholars. The paper tries to construct the market mechanism which can make the vulnerable people to involve in the emission trading. The vulnerable people can buy American put option in the emission trading market. When the price of the emission runs below the contract price, the vulnerable people can get the benefit through executing the option. When the price of the emission runs above the contract price, the vulnerable people can give up the right. The binomial tree option pricing model can help the vulnerable people to make a decision through the analysis of the worth of the American put option.
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We present a parallel algorithm that computes the ask and bid prices of an American option when proportional transaction costs apply to trading in the underlying asset. The algorithm computes the prices on recombining binomial trees, and is designed for modern multi-core processors. Although parallel option pricing has been well studied, none of the existing approaches takes transaction costs into consideration. The algorithm that we propose partitions a binomial tree into blocks. In any round of computation a block is further partitioned into regions which are assigned to distinct processors. To minimise load imbalance the assignment of nodes to processors is dynamically adjusted before each new round starts. Synchronisation is required both within a round and between two successive rounds. The parallel speedup of the algorithm is proportional to the number of processors used. The parallel algorithm was implemented in C/C++ via POSIX Threads, and was tested on a machine with 8 processors. In the pricing of an American put option, the parallel speedup against an efficient sequential implementation was 5.26 using 8 processors and 1500 time steps, achieving a parallel efficiency of 65.75%.
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.
