Pricing and Hedging of Cliquet Options and Locally Capped Contracts

This paper provides a new approach for pricing and hedging popular highly path-dependent equity-linked contracts. We illustrate our technique with two examples: the locally capped contracts (a popular design on the exchange-listed retail investment contracts on the American Stock Exchange) and the cliquet option (extensively sold by insurance companies). Wilmott [Wilmott Magazine, 2002, pp. 78--83] describes these types of contracts as the “height of fashion in the world of equity derivatives.” Existing literature proposes methods based on partial differential equations, Monte Carlo techniques, or Fourier analysis. We show that there exist semi-closed-form expressions of their prices as well as of the hedging parameters.