Pricing And Hedging Up-and-out Barrier Option

Barrier options as typical exotic options are trading frequently at domestic OTC(over-the counter)market,the jumping structure and path dependence of barrier options make the hedge method always become a difficult problem for industries.In this paper,We conduct a comparative analysis of pricing the up-and-out barrier options of the CSI 300 index and the pricing results show that there is no significant difference in the value of the barrier options based on the analytical solution or Monte Carlo simulation.This gives us a reminder that the indifference of market pricing makes the option products quotation trade are same between the agencies,and it is necessary to do a good hedging work through continuous issuance of option products.Most important of all is the lower the hedge cost,the higher the profit.Unlike European options,when hedging barrier option,Delta has a dramatic change near the barrier price and its absolute value is larger.So the delta dynamic hedging cost is higher and the extreme cost is larger.Through the analytical solution of Black-Scholes-Merton model and numerical solution of Monte Carlo simulation method,we price the barrier options and analyze the options Greeks changes,enumerate the static replicate maximal cost and deduce options dynamic barrier out-shift boundary according to the variation of delta.The purely moving boundaries,butterfly-moving boundaries,spread replication moving boundaries,and ergodic trigger-outbound boundaries are proposed to reduce the risk of barrier option sellers.The average hedging cost and extreme effect are analyzed for simulation 10000 index path.The simulation results show that the order of average cost of different hedge method from low to high are:the ergodic triggering shifting,pure shifting,butterfly replication shifting,spread replication shifting.In order of reducing the effectiveness of extreme effects are:the ergodic triggering shifting,butterfly replication shifting,spread replication shifting and pure shifting.In addition,for the actual sample hedging work,we select 2011-2016 actual CSI 300 index to back-test and verify whether hedge strategy have its efficiencybase on the method of Stop-Loss Start-Gain strategy and appropriate shift price barriers.The effective hedge strategy is well reflected from the lower average cost hedge,smooth hedge extreme cost and quantile results.The results reflect the hedge strategy performs well and realize effective hedging of the barrier options.