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...

A bank's stock price is modeled as a call option on the spread of random assets over random liabilities. The logarithm of assets and liabilities are jointly modeled as driven by four variance gamma processes and this model is estimated by calibrating to quoted equity options seen as compound...