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