Generalized Binomial Trees

We consider the problem of consistently pricing new options given the prices of related options on the same stock. The Black-Scholes formula and standard binomial trees can only accommodate one related European option which then effectively specifies the volatility parameter. Implied binomial trees can accommodate only related European options with the same time-to-expiration.The generalized binomial trees introduced here can accommodate any kind of related options (European, American, or exotic) with different times-to-expiration.