BFS 2002

Poster Presentation

Hedging Errors and Mispecified Volatility

Iliana Anagnou, Stewart Hodges

The paper provides a general representation for the errors of delta hedging derivatives contracts under misspecified asset price processes. A new 'Greek' is developed which quantifies the dependence between the prospective hedging errors and the volatility forecast errors. This analysis can be applied to any contingent claim that can be spanned under a general diffusion process. The hedging errors are studied in more detail for a standard vanilla option, a geometric average rate option, and an up and out call option with a continuous-time monitored barrier. Two alternative approaches are provided for deriving the conditional and unconditional distribution of hedging errors: binomial tree and kernel estimation. The binomial tree method exploits the Markovian nature of hedging errors. By evolving hedging errors forward, all the moments of the conditional and unconditional distributions are obtained. Alternatively, kernel estimation provides local estimates and confidence intervals for hedging errors. The analysis provides techniques for obtaining information on the absolute and relative difficulties of hedging different instruments or portfolios of instruments.