The modified sequential hedging strategy: hedger's loss distribution

We study the distribution of hedging costs for the seller of an American call option who uses the modified sequential hedging strategy. Buying and selling of the underlying asset is done when the underlying asset's price intersects a band that includes the exercise price. We obtain analytic expressions for conditional and unconditional distribution functions of the hedger's costs. The conditional distribution is found for a known number of intersections of the band by the underlying asset's course trajectory. We propose an algorithm for estimating the quantile of the cost distribution (VaR criterion) that uses the quantile values for the hedger's conditional cost distribution.