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Published online by Cambridge University Press: 19 September 2009
All general laws are attended with inconveniences, when applied to particular cases.
David Hume, “Of the Rise and Progress of the Arts and Sciences”The no-arbitrage principle says there should be no free lunch. Simple as it is, this principle supplies the essential argument for option pricing. After the argument is presented in Section 8.1, several important option pricing relations will be derived.
The Arbitrage Argument
A riskless arbitrage opportunity is one that, without any initial investment, generates nonnegative returns under all circumstances and positive returns under some circumstances. In an efficient market, such opportunities should not exist. This no-arbitrage principle is behind modern theories of option pricing if not a concept that unifies all of finance [87, 303]. The related portfolio dominance principle says that portfolio A should be more valuable than portfolio B if A's payoff is at least as good under all circumstances and better under some circumstances.
A simple corollary of the no-arbitrage principle is that a portfolio yielding a zero return in every possible scenario must have a zero PV. Any other value would imply arbitrage opportunities, which one can realize by shorting the portfolio if its value is positive and buying it if its value is negative.
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