Lookback options are path-dependent options. In general, the binomial tree methods, as the most popular approaches to pricing options, involve a path dependent variable as well as the underlying asset price for lookba...Lookback options are path-dependent options. In general, the binomial tree methods, as the most popular approaches to pricing options, involve a path dependent variable as well as the underlying asset price for lookback options. However, for floating strike lookback options, a single-state variable binomial tree method can be constructed. This paper is devoted to the convergence analysis of the single-state binomial tree methods both for discretely and continuously monitored American floating strike lookback options. We also investigate some properties of such options, including effects of expiration date, interest rate and dividend yield on options prices, properties of optimal exercise boundaries and so展开更多
In this paper we are concerned with the pricing of lookback options with American type constrains. Based on the differential linear complementary formula associated with the pricing problem, an implicit difference sch...In this paper we are concerned with the pricing of lookback options with American type constrains. Based on the differential linear complementary formula associated with the pricing problem, an implicit difference scheme is constructed and analyzed. We show that there exists a unique difference solution which is unconditionally stable. Using the notion of viscosity solutions, we also prove that the finite difference solution converges uniformly to the viscosity solution of the continuous problem. Furthermore, by means of the variational inequality analysis method, the O（△t ＋ △x^2）-order error estimate is derived in the discrete L2-norm provided that the continuous problem is sufficiently regular. In addition, a numerical example is provided to illustrate the theoretical results.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
基金Supported by National Science Foundation of China
文摘Lookback options are path-dependent options. In general, the binomial tree methods, as the most popular approaches to pricing options, involve a path dependent variable as well as the underlying asset price for lookback options. However, for floating strike lookback options, a single-state variable binomial tree method can be constructed. This paper is devoted to the convergence analysis of the single-state binomial tree methods both for discretely and continuously monitored American floating strike lookback options. We also investigate some properties of such options, including effects of expiration date, interest rate and dividend yield on options prices, properties of optimal exercise boundaries and so
基金supported in part by the National Basic Research Program(2007CB814906)the National Natural Science Foundation of China(10771031,10471019,10471103,and 10771158)+1 种基金Social Science Foundation of the Ministry of Education of China(Numerical methods for convertible bonds,06JA630047)Tianjin Natural Science Foundation(07JCYBJC14300)and Tianjin University of Finance and Economics
文摘In this paper we are concerned with the pricing of lookback options with American type constrains. Based on the differential linear complementary formula associated with the pricing problem, an implicit difference scheme is constructed and analyzed. We show that there exists a unique difference solution which is unconditionally stable. Using the notion of viscosity solutions, we also prove that the finite difference solution converges uniformly to the viscosity solution of the continuous problem. Furthermore, by means of the variational inequality analysis method, the O（△t ＋ △x^2）-order error estimate is derived in the discrete L2-norm provided that the continuous problem is sufficiently regular. In addition, a numerical example is provided to illustrate the theoretical results.
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.
