Completing Markets: Options and Long-Lived Securities

General Equilibrium
Information and Uncertainty
Financial Economics

Interactive Tutorial

Options are one of the more interesting securities to which arbitrage reasoning can be applied. (European) options, recall, are assets who derive their value from an underlying security, thus they have a return structure ro = [max(0, r1 - c), max(0, r2 - c), .., max(0, rS-c)] where r1, r2, .., rS are the returns on the underlying security and c is the "strike" price. The strike price is the asset price at which the owner of the option is entitled to buy (if a call option) or sell (if a put option) a unit of an underlying security if he decides to "exercise" it. One of the more interesting results, as stressed by Stephen Ross (1976), is that we can use options to "complete" incomplete markets: specifically, we can construct options to span a space when there are an insufficient number of fundamental assets.