Market-Consistent Prices for General Payoffs

Abstract

In an arbitrage-free market it is possible to price replicable payoffs in a market-consistent manner by way of replication. Similar to what we did in Chap. 8 for the single-period model, in this chapter we extend the concept of a market-consistent price to payoffs that are not replicable. We provide several different descriptions of the set of market-consistent prices and show that the price at which rational sellers and buyers will contemplate transacting a nonreplicable payoff at a certain point in time needs to respect some natural bounds. The upper bound is called the superreplication price and corresponds to the threshold above which no buyer should be willing to buy, while the lower bound is called the subreplication price and corresponds to the threshold below which no seller should be willing to sell.