Abstract
ABSTRACTWe show that in a discrete price and discrete time model for option pricing, specifically that given by the Cox–Ross–Rubinstein model, the arbitrage price of a European call option can depend on parameters other than volatility (the standard deviation of the log asset price). We provide two theorems to illustrate this phenomenon. Our first theorem considers two securities with the same volatility so that at a specified time n0, with probability near 1, the two securities are equal. If their call options differ, both the discounted securities will be martingales. Our second theorem considers two securities with the same volatility so that at times n = 0, ..., N − 1 the securities are equal with probability near 1. If their call options differ, one of the discounted securities will be a martingale and the other discounted security will be a supermartingale.
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