Risk Management Using Quasi–static Hedging

In this paper, we try to develop a comprehensive theory of risk management for illiquid trading instruments and exotics by examining the consequences of a quasi–static hedging strategy. In contrast to a static hedging strategy, in which an initial hedge once executed is kept in place for the life of the trade, and a dynamic hedging strategy, in which hedges are frequently adjusted over the life of the trade, a quasi–static hedging strategy utilizes hedge adjustments but tries to minimize the frequency. Almost all the examples studied in the framework introduced here take this minimization to the extreme by limiting hedge adjustments to at most one during the life of a trade. We examine the application of this approach to long–dated forwards, long–dated options and exotic options such as cliquet and barriers. The model we present for barriers is a new generation of the Derman–Ergener–Kani approach which combines the flexibility of the approach with a sizable increase in model independence.