Closed form valuation of American chained knock-in options

•We find relation between American chained options and American knock-in options.•We get analytic formula for the value of American chained barrier options.•We numerically priced American chained options using recursive iteration method.

In this paper, we study pricing of American chained knock-in option. Chained barrier option is a new type of barrier option with two barrier levels. A knock-in American chained barrier option under a trigger clause is an option contract in which the option holder receives an American knock-in option conditional on the underlying asset price breaching a specified barrier level. We derive analytic valuation formulas for knock-in American chained options under the Black-Scholes pricing framework by using reflection principle and formulas for knock-in American options. Furthermore, we present some numerical solutions and plots of the value of knock-in American chained options.