Shortfall-Risk Minimizing Hedging Based on MCMC Method

Many researchers have studied the multi-period shortfall-risk minimizing hedging problem under jump-diffusion settings, however, up to now, there has not been many literatures to directly present the analytic solution for such a hedging problem. In this paper, defining the terminal shortfall as hedging risk, we research the minimal shortfall-risk hedging problem of European option by means of MCMC method. Firstly, we look on the underlying asset's positions held at each strategy rebalancing moment during option's maturity as a random vector; then, we aptly construct this random vector's conditional joint probability density function, from which we sample a Markov chain, according to the Bayes principle and Ergodic theorem, the drawn Markov chain will congregate around the optimal strategy with higher probability and converge to it, thus, it's reasonable to substitute the optimal hedging position with the averaged value of this Markov chain; finally, experimental analysis results illustrate that our method is not only feasible but convenient to manipulate while being helpful and referential to hedging practice.