The Cox, Ross, and Rubinstein binomial model is generalized to the multinomial case. Limits are investigated and shown to yield the Black-Scholes formula in the case of continuous sample paths for a wide variety of complete market structures. In the discontinuous case a Merton-type formula is...

Complex positions on multiple underliers are hedged using the options surface of all underliers. Hedging objectives follow Cherny and Madan (2010) by minimizing ask prices for which post hedge residual risks are acceptable at prespecified levels. It is shown that such hedges require one to use a...