Greeks Estimation Of Derivatives Under The Hyper Dual Number Method

With the increasing variety and volume of China’s derivatives trading and the need of COVID-19’s risk management,it is becoming more frequent for financial practitioners to manage the option positions and hedge risks with the Greeks.For option traders,the Greeks estimation results are helpful to manage the position risk,but also help to build a risk hedging model to further control the profit and loss.The path-dependent options-American options and Asian options,can effectively resist the risks brought by market manipulation,which are very critical in stabilizing the financial market or maintaining the production cost of enterprises.However,the traditional finite difference method,likelihood ratio method,pathwise method,etc.have a certain lack of accuracy in the estimation of Greeks,especially in the aspect of second-order Greeks.Based on this,the thesis estimates the first-order and second-order Greeks of path-dependent options by introducing Hyper dual number.The main research contents are as follows:First of all,this thesis sorts out the literature on option models and pricing theories to determine the pricing models and methods of American options and Asian options in this thesis.Then,it introduces the definition of Greeks and option Greeks estimation theory,analyzes the advantages and disadvantages of each Greeks estimation method,and imports the artificial complex—— Hyper dual number to form the HDN method of estimating the Greeks.Next,the first-and second-order Greeks estimation algorithm and basic implementation steps are designed for Geometric average Asian options with standard analytical formulas,Arithmetic average Asian options with Monte Carlo pricing,and binary tree-priced American options by using the HDN method and other methods respectively in this thesis and the corresponding numerical experiments are carried out.Finally,the numerical experiment results of each method and the resource consumption of some numerical experiments are shown,and the estimation effect of each method on the first-order Greeks delta,vega and the second-order Greeks gamma and vomma is analyzed.Based on the results of numerical experiments,it is ultimately found that compared with methods such as finite difference method,the HDN method is superior in the estimation of the second-order Greeks vomma rarely studied in the past,which is manifested in two aspects: on the one hand,Geometric average Asian options with analytical pricing formulas fluctuate slightly but the estimation of vomma are accurate;on the other hand,the estimation results of the Arithmetic average Asian options priced by the Monte Carlo numerical method and the American options priced by the binary tree numerical method are accurate and stable.In addition,the HDN method estimates the first-order Greeks delta and vega with higher accuracy and outstanding stability.The HDN method used in this thesis provides a brand-new method for Greeks estimation,especially for the Greeks estimation with volatility as the core,which is rarely studied in the past literature reviews.This method is easy to understand,has high precision,and is highly scalable.It is not only valuable in Greeks estimation,but can also be used as an alternative to option pricing.Therefore,the theoretical study of Greeks estimation method and Greeks risk management practice in this thesis are of great significance.