OPTIMAL HEDGING OF PATH-DEPENDENT OPTIONS IN DISCRETE TIME INCOMPLETE MARKET

Abstract. We consider hedging of a path-dependent European style option with convex continuous payoff in a discrete time incomplete market, where underlying stock price jumps are distributed over a bounded interval. The incompleteness of the market produces an interval of no-arbitrage option prices for the path-dependent option. Upper and lower bounds for the no-arbitrage price interval are developed. Explicit formulas for a no-arbitrage option price and a non-self-financing hedging strategy are given. Each non-self-financing hedging strategy produces an accumulated residual amount. Theoretical results are applied to the case of an arithmetic Asian option. A numerical algorithm for constructing the non-self-financing hedging strategy that maximizes the accumulated residual amount is developed. The algorithm is tested on various underlying stocks and the Standard & Poor 500 Index. 1