Pricing an Accumulator with Continuous or Discrete Barrier

Abstract

The low interest rate environment of recent years has sent many investors looking for ways to enhance returns. This has stimulated the creation of investment products with what were once known as “exotic” payoff patterns. These products tend to involve exposure to a risky security like a stock index, overlaid with a combination of guarantees and barriers designed to appeal to the target investor audience. Small investors, and many fiduciaries such as small pension funds, are rarely in a position to evaluate the highly path-dependent payoffs on such securities. In this article, the authors analyze a somewhat different product, the “accumulator” contract. This product is actually a formalized plan to build up a holding in some specific asset, typically a stock, through a series of purchases over time. In a typical example, the buyer commits to buy some number X of shares per day at a fixed price that is initially set below the current market price. If the market price subsequently falls below the contract price, the required purchase amount is doubled. But if the market price goes too far above the strike price, the contract terminates. The article presents valuation formulas for some standard variants and shows empirically that accumulator contracts are priced in the market at levels that tend to be quite favorable to the issuer.