Pricing and hedging barrier options based on Merton model and Monte Carlo simulation

Barrier options as typical exotic options are trading frequently at the domestic OTC (over-the counter) market, whose jumping structure and path dependence make the hedge method a constant problem for the industry. Here a barrier options hedge strategy applicable to current domestic financial market was designed by a comparative analysis for pricing the up-and-out barrier options of the CSI 300 index. The barrier options price and the Greeks change were analyzed through the analytical solution of the Black-Scholes-Merton model and numerical solution of the Monte Carlo simulation method. According to the simulated 10 000 index path of hedge and the variation of delta, the static replicate maximal cost was enumerated and options dynamic barrier out-shift boundary was deduced for analyzing the average hedge cost and extreme effect. 2011～2016 actual CSI 300 was selected to back-test and verify the effectiveness of the hedge strategy. The results show that the hedge average cost is significantly reduced under the hedge idea of the traversal trigger outward moving barrier boundary, and that the distribution of the hedge extremes and quantiles is relatively smooth, which reflects the good performance of the hedge strategy and the effective hedge of the barrier option.