The Bermudan option pricing problem with variable transaction costs is considered for a risky asset whose price process is derived under the information-based model. The price is formulated as the value function of an...The Bermudan option pricing problem with variable transaction costs is considered for a risky asset whose price process is derived under the information-based model. The price is formulated as the value function of an optimal stopping problem, which is the value function of a stochastic control problem given by a non-linear second order partial differential equation. The theory of viscosity solutions is applied to solve the stochastic control problem such that the value function is also the solution of the corresponding Bellman equation. Under some regularity assumptions, the existence and uniqueness of the solution of the pricing equation are derived by the application of the Perron method and Banach Fixed Point theorem.展开更多
An efficient option pricing method based on Fourier-cosine expansions was presented by Fang and Oosterlee for European options in 2008, and later, this method was also used by them to price early-exercise options and ...An efficient option pricing method based on Fourier-cosine expansions was presented by Fang and Oosterlee for European options in 2008, and later, this method was also used by them to price early-exercise options and barrier options respectively, in 2009. In this paper, this method is applied to price discretely American barrier options in which the monitored dates are many times more than the exercise dates. The corresponding algorithm is presented to practical option pricing. Numerical experiments show that this algorithm works very well and efficiently for different exponential Levy asset models.展开更多
An efficient and accurate numerical method, which is called the CONV method, was proposed by Lord et al in [1] to price Bermudan options. In this paper, this method is applied to price Bermudan barrier options in whic...An efficient and accurate numerical method, which is called the CONV method, was proposed by Lord et al in [1] to price Bermudan options. In this paper, this method is applied to price Bermudan barrier options in which the monitored dates may be many times more than the exercise dates. The corresponding algorithm is presented to practical option pricing. Numerical experiments show that this algorithm works very well for different exponential Lévy asset models.展开更多
The empirical study shows that the return rate of the stock price has a long memory, which can be described by fractal Brown motion. The fact that fractal Brown motion does not have the characteristics of Markov makes...The empirical study shows that the return rate of the stock price has a long memory, which can be described by fractal Brown motion. The fact that fractal Brown motion does not have the characteristics of Markov makes the American option value depends on the price change path of the underlying asset. And the ordinary American option pricing model underestimates the American option value. In order to fully reflect the long memory of the underlying asset return rates, we propose fractal American option pricing model, fractal Bermuda option pricing model, and a fractal combination of American option pricing model. Fractal American option value is greater than the ordinary American option value.展开更多
文摘The Bermudan option pricing problem with variable transaction costs is considered for a risky asset whose price process is derived under the information-based model. The price is formulated as the value function of an optimal stopping problem, which is the value function of a stochastic control problem given by a non-linear second order partial differential equation. The theory of viscosity solutions is applied to solve the stochastic control problem such that the value function is also the solution of the corresponding Bellman equation. Under some regularity assumptions, the existence and uniqueness of the solution of the pricing equation are derived by the application of the Perron method and Banach Fixed Point theorem.
基金supported by the research grants (UL020/08-Y4/MAT/JXQ01/FST and MYRG136(Y1-L2)-FST11-DD) from University of Macao
文摘An efficient option pricing method based on Fourier-cosine expansions was presented by Fang and Oosterlee for European options in 2008, and later, this method was also used by them to price early-exercise options and barrier options respectively, in 2009. In this paper, this method is applied to price discretely American barrier options in which the monitored dates are many times more than the exercise dates. The corresponding algorithm is presented to practical option pricing. Numerical experiments show that this algorithm works very well and efficiently for different exponential Levy asset models.
文摘An efficient and accurate numerical method, which is called the CONV method, was proposed by Lord et al in [1] to price Bermudan options. In this paper, this method is applied to price Bermudan barrier options in which the monitored dates may be many times more than the exercise dates. The corresponding algorithm is presented to practical option pricing. Numerical experiments show that this algorithm works very well for different exponential Lévy asset models.
文摘The empirical study shows that the return rate of the stock price has a long memory, which can be described by fractal Brown motion. The fact that fractal Brown motion does not have the characteristics of Markov makes the American option value depends on the price change path of the underlying asset. And the ordinary American option pricing model underestimates the American option value. In order to fully reflect the long memory of the underlying asset return rates, we propose fractal American option pricing model, fractal Bermuda option pricing model, and a fractal combination of American option pricing model. Fractal American option value is greater than the ordinary American option value.
