Application Of Gauss-Hermite Quadrature Algorithm To Bermudann Put Option Pricing Problem

Option is a financial derivative that buys and sells the underlying asset at an agreed price and date,giving the buyer rights(not obligations).Options are often used as a form of compensation or as part of complex financial transactions.As such,they are also a form of asset whose valuation can depend on complex relationships between the value of the underlying asset,maturity dates,market fluctuations and other factors.With the development of the financial market,customers’ demands for the financial market have become more and more complex.Standard options have been unable to meet the changes of customers’ demands.In order to better meet customers’ demands and avoid risks,some financial companies have innovatively developed many new trading varieties based on standard options.These new trades can vary in terms of payout and timing,and are often more complex than regular call and put options,such as Bermudan.Bermudan option refers to an option that can be exercised on certain specified dates before the expiration date.It is the mainstream variety of over-the-counter options in my country,and it is an exotic option between European options and American options.It can be regarded as a mixture of two options.Due to the path-dependent characteristics of Bermudan options,the pricing problem of Bermudan options has attracted the attention of many scholars and financial workers.Therefore,it is of practical significance to select Bermudan put options as the research object in this paper.Based on Lim’s research in 2014,this paper will use the Gauss-Hermite quadrature method to construct a new pricing method for Bermudan put options,and make an approximate calculation of the option value.In this paper,the gradient descent method is used to find the optimal execution boundary point of Bermudan put option.After obtaining the optimal execution boundary of Bermudan put option by gradient descent method,the option value of each observation time is divided into the execution part and the holding part.And use the Gauss-Hermite quadrature algorithm to approximately solve the holding part.The price of the underlying asset is the best strike frontier point for a Bermudan put option when the hold value and strike value of the option are equal.Through experiments,it is proved that the method in this paper to price Bermudan put option and use gradient descent method to find the best execution boundary point is effective.The experimental results show that the method in this paper can improve the operation rate under the condition of ensuring stable convergence,and after changing a certain parameter,it can still improve the operation rate while the stable point converges.