Static Replication Vs Dynamic Hedging

Hedging of options is an issue of great concern in the derivatives market,and the hedging methods vary significantly depending on the type of option due to the different movements of the underlying asset involved.The mainstream hedging strategies include static replication and dynamic delta hedging,and how option issuers choose hedging strategies to hedge their exposures when issuing options is a key consideration.Currently,the OTC derivatives market is growing rapidly and barrier options are a popular product in the OTC derivatives market,including complex barrier options such as shark fin options and snowball options.In terms of barrier option hedging strategy selection,the static replication method does not require adjustment after the replication portfolio is determined at the beginning of the period,but the hedging effect is greatly influenced by the number and type of options.In contrast,while dynamic delta hedging allows for flexible portfolio adjustment,the adjustment of delta may change drastically when the spot price approaches the barrier price,resulting in high hedging costs when options are knocked out.This paper investigates the pricing and hedging strategies of standard options,standard barrier options and snowball options based on the underlying asset obeying the standard Brownian motion or Mertonjump diffusion model,and compares the advantages,disadvantages and feasibility of static replication and dynamic delta hedging strategies.The paper can be divided into three major parts.The first part explores the Delta hedging effect of European options when the underlying asset obeys the standard Brownian motion or Merton-jump diffusion model.The second part explores the performance of static replication and delta hedging of upward knock-out call options.In terms of static replication,the errors in portfolio value and barrier option value are compared for different knockout moments and different number of option replications,and an optimization method for static replication of a fixed number of option portfolios is proposed.Experiments show that the improved option portfolios have smaller errors and better hedging effects.In terms of dynamic hedging,the hedging cost errors are compared at different knock-out moments and different hedging frequencies,and the effect of changes in hedging costs on the variation of errors is explored.Finally,the advantages and disadvantages of static replication and dynamic hedging of standard barrier options are compared and analyzed.The third part explores static replication and dynamic hedging of snowball options and briefly discusses a semi-static replication method that combines static replication and dynamic hedging.Based on theoretical and practical analysis and research,static replication and delta hedging of options are feasible in the domestic derivatives market,including barrier options with complex terms.This paper explores and compares different hedging methods to provide a reference for option managers or investors to manage risk.