%0 Journal Article %A Mark A. Cassano %T How Well Can Options Complete Markets? %D 2001 %R 10.3905/jod.2001.319171 %J The Journal of Derivatives %P 7-17 %V 9 %N 2 %X An interesting and important question about options is how much they expand the range of investment opportunities in the market. In the Black-Scholes framework, the market is already “dynamically complete”: options are redundant assets because any option payoff can be replicated by dynamically trading the underlying asset and riskless bonds. But in the real world, options do expand investment opportunities, because the replication strategy entails infinite trading and infinite transaction costs. The next question is whether options can make the market statically complete, in that any possible contingency can be perfectly hedged by a static portfolio of options. Theory shows that this is true, but that it requires an infinite number of options with a continuum of different strikes. In this article, Cassano considers how close one can get to the ideal of static completeness using just a small number of options. Since not all risk can be hedged, how close is “close” depends on the investor’s utility function. But Cassano shows that under standard assumptions with risk aversion in a range that is commonly assumed, it only takes a handful of different options, say four or five, to achieve such near-completeness that it would only be worth a few pennies per hundred dollars of wealth to a typical investor to go the rest of the way to a fully complete market. %U https://jod.pm-research.com/content/iijderiv/9/2/7.full.pdf