ABSTRACT
This chapter considers the assumptions underlying the derivation of the no-arbitrage condition. The assumptions are analyzed from two viewpoints. First, if an assumption is dropped, can a different no-arbitrage condition be derived? If it can, is the assumption concerned a simplifying assumption, and gross violations of the assumption encompassed by a more general formula? Second, to what extent is the assumption met in reality, and how large is the effect of violation on the validity of the no-arbitrage condition? If the effects are large, and a more general no-arbitrage condition relaxing the assumption cannot be derived, the validity of the no-arbitrage condition is conditional on the relevant assumption. The derivation of the no-arbitrage condition requires that the risk free borrowing and lending rates are equal. If there is no marking to the market, variations in the riskless interest rate have no effect on the no-arbitrage condition.
