Effectiveness Analysis Of Numerical Methods For Option Pricing

An option is a contract that gives buyers and sellers rights and obligations.The buyer has the right to decide whether to purchase a commodity at the agreed price at the expiry date,and the seller must fulfill the obligation to complete the transaction at the buyer's will.Due to the existence of option fee,option is essentially a commodity with the attribute of price,and the level of option price directly affects the profit and loss of the sale and purchase.Therefore,the issue of option pricing is also the core issue of option trading.The early options products were not respected by the market for various reasons.The establishment of the Chicago Options Exchange did not change this situation until 1973.It established a trading system that uses standardized option contracts and follows a standardized process.Guaranteed Exchange Circulation.At the time,the Bretton Woods system was disintegrating,and the volatility of world financial markets was intensifying.Against this background,various types of financial derivatives emerged endlessly,and financial options were reborn.On February 9,2015,the Shanghai Stock Exchange also officially launched the first domestic financial options product: the Shanghai 50 ETF Option.It not only enriches investors' methods of speculative arbitrage or hedging,but also serves as a tool for risk management,so it is favored by investors.Due to the characteristics of zero-sum game and high leverage,the price of SSE 50 ETF options has become a very sensitive factor.In order to exert its functions and standardize market management,it is also necessary for investors to make rational judgments and correctly price them.It seems particularly important.The issue of option pricing has always been one of the most complicated issues in the financial field.Today,although option pricing theories are very mature and there are various pricing models,their conclusions mostly come from research on foreign markets,and Whether these models are suitable for China's options market is still worth examining.Options pricing methods usually include partial differential methods and numerical methods.In the case of continuous time,a stochastic differential equation can be used to describe the movement path of the underlying asset price,and the option as its derivative,the problem of pricing it is equivalent to solving the partial differential equation.When there is no analytical solution to the equation,numerical methods can be used to simulate the movement path of asset prices to solve the option pricing problem.Numerical methods are a type of methods with a wider range of application and lower use thresholds.At present,there are few studies on using numerical methods to price SSE 50 ETF options.Therefore,this article cuts in from this perspective,and aims to find the numerical method that is most suitable for pricing SSE 50 ETF options.With the help of previous literature,this paper sorts out the development process of option pricing theory and summarizes the development of domestic financial option market.Subsequently,this paper focuses on the relevant theory and calculation process of the three options pricing method of binary tree option pricing model,Monte Carlo simulation and finite difference method.Based on China's Shanghai 50 ETF and China Securities 50 ETF options 10001521.SH,10001597.SH,10001598.SH three contracts from December 3,2018 to June 21,2019,with 133 closing price data as a research sample,and using python language to write an arithmetic program,based on the Shanghai Stock Exchange 50 ETF closing price data to simulate the Shanghai 50 ETF options Price,through linear regression analysis to observe the linear relationship between the theoretical price and the actual price time,and compare the degree of fit through the judgment coefficient(adjusted).Then through the index analysis method,compare the gap between the theoretical price and the actual price simulated by the three numerical methods,and then verify the validity of the numerical method for the pricing of the Shanghai Stock Exchange 50 ETF option,and at the same time compare the fit and error of the three methods.To find a more efficient way of pricing.The final research results show that the Monte Carlo simulation method is more suitable for the pricing of 50 ETF options in terms of pricing accuracy and calculation time.