Optimal Dynamic Hedging of Multi-Asset Options

Abstract

Hedging and valuing multi-asset options are analyzed using the Optimal Hedge Monte-Carlo method. The average cost of hedging and the residual risks are related to the stochastic description of the underlying assets, their dependence structure, and to the option contract details. A long position in a basket of the underlying assets mixed in proportions to their hedge ratios is employed to assess a bounding rate of return on risk-capital (i.e., a hurdle rate) for the option trader-hedger. That hurdle rate is employed to assess bounding values of multi-asset derivative positions while accounting for hedging costs and the inevitable hedge slippage that determines the derivative trader's risk-capital. Sample calculations are provided for two-asset options where the option trader-hedger is long correlation and short correlation, such as best-of and worst-of options. The differences in hedging strategies between such options and junior and senior basket-put tranches are delineated. The dual roles of fat-tails for individual assets and uncertainty of realized correlation in controlling the irreducible hedging errors are also described.