
 Optimal Dynamic Hedging of Cliquets by Andrea Petrelli of CreditSuisse, May 2008 Abstract: Analyzed here is a Cliquet put option (ratchet put option) defined as a resettable strike put with a payout triggered by the reference asset falling below a specified fraction of its value at a prior lookback date. The hedging strategy that minimizes P&L volatility over discrete hedging intervals is assessed. Examples are provided for an asset exhibiting jumpy returns (kurtosis > 3) and temporal correlation between the squared residual returns. The limited liquidity of the asset limits the discrete hedging frequency. Each of the realities of discrete hedging intervals and fattailed asset return distributions render the attempted replication imperfect. A residual risk dependent premium is added to the average cost of attempted replication (i.e., average hedging cost) based on a target expected return on risk capital. By comparing the P&L distribution of a derivative sellerhedger with that of a deltaone trader holding a long position in the underlying asset, relativevalue based bounds on pricing of vanilla options and Cliquets are presented. JEL Classification: G13, G11, D81. Keywords: GapRisk, Cliquet, CrashCliquet, Kurtosis, Hedging, ResidualRisk, OptionTraders'sP&L. Books Referenced in this paper: (what is this?) 