Market-Consistent Prices for Replicable Payoffs

Abstract

This chapter is devoted to extending to the multi-period setting the theory of market-consistent prices for replicable payoffs that was laid out in Chap. 6 for a single-period economy. Because of the dynamic nature of the setting, financial contracts can now mature at any date after the initial date and their prices can be determined at any date prior to their maturity. The key requirement enabling a rich valuation theory is that it should not be possible to make a riskless profit by trading in the basic securities, i.e., price and payoff arbitrage opportunities should not exist. Similar to the single-period case, the non-existence of price arbitrage opportunities is equivalent to the validity of the multi-period version of the Law of One Price. In this case, a conditional linear pricing functional exists for every date and every maturity. Moreover, markets in which no payoff arbitrage opportunities exist can be characterized by the strict positivity of the pricing functionals.