A modified binomial tree method for currency lookback options
Lookback options are path dependent options whose payoffs depend on the maximum or the minimum of the underlying asset price during the life of options. \textit{Cox}, \textit{Ross} and \textit{Rubinstein} [J. Financ. Econ. 7, No. 3, 229--263 (1979; Zbl 1131.91333)] have proposed the `binomial tree method' as a discrete model and it is the most, popular numerical approach to the pricing option. Since lookback options are mostly structured with a foreign exchange as an underlying variable, such options are treated with continuously monitoring. It has also been observed that the binomial tree method for currency lookback options converges very slowly. In this paper the author has developed a more efficient scheme on the basis of PDE approach known as the modified binomial tree method. This method possesses one order of accuracy and its efficiency is demonstrated by numerical experiments. It has been shown that the values of currency lookback options computed from the modified binomial tree method converge to the true solutions of the corresponding continuous model. Due to consistency, the convergence can be directly deduced by the Lax theorem for European cases. But for American currency lookback put options, it causes some difficulties.
scientific article; zbMATH DE number 1530090