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Optimal Static-Dynamic Hedges for Exotic Options under Convex Risk Measures

Ronnie Sircar (Princeton University)

We study the problem of optimally hedging exotic derivatives positions in an incomplete market using derivatives as well as basic assets such as stocks. In incomplete markets, we may want to use derivatives, as a proxy for trading volatility, for instance, but they should be traded statically, or relatively infrequently, compared with assumed continuous trading of stocks, because of the much larger transaction costs. The performance of the static-dynamic hedging strategies is quantified by a convex risk measure. We establish conditions for the
existence of an optimal static position for general convex risk measures, and then analyze in detail the case of expected shortfall with a power loss function. We illustrate the computational challenge of finding the market-adjusted risk measure in a diffusion model for an option on a non-traded asset.

Joint work with Aytac Ilhan and Mattias Jonsson.

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