VALUE-AT-RISK ESTIMATION FOR DYNAMIC HEDGING

In this work, we develop an efficient methodology for analyzing risk in the wealth balance (hedging error) distribution arising from a mean square optimal dynamic hedge on a European call option, where the underlying stock price process is modeled on a multinomial lattice. By exploiting structure in mean square optimal hedging problems, we show that moments of the resulting wealth balance may be computed directly and efficiently on the stock lattice through the backward iteration of a matrix. Based on this moment information, convex optimization techniques are then used to estimate the Value-at-Risk of the hedge. This methodology is applied to a numerical example where the Value-at-Risk is estimated for a hedged European call option on a stock modeled on a trinomial lattice.