Pricing American-style Parisian Option Based On The Least Squares Monte Carlo Approach

China's economy has entered a new stage of development.The economic structure has begun to transform.In the development of the financial industry,there are also many new trends of system reform and inclusive finance.With the increase of the number of Listed Companies in our country,many listed companies have introduced executive options,which means giving the executive of the company the right to buy a certain number of company shares at the agreed price in a specific period of operation.The advantage of executive option is that it can form the interest community of shareholders and executives and maximize the value of the company.However,common executive options have the risk of stock price manipulation,which is disadvantageous to the owner of the enterprise.Therefore,the introduction of American-style Parisian Option in non-classical options contracts is a better choice.American-style Parisian options need certain price trigger conditions and duration requirements to knock in or knock out.After adding American characteristics,option holders are given the right to execute flexibly before and after meeting the trigger conditions.For the owners and executives of enterprises,it is a win-win incentive.Therefore,it is particularly important to study the pricing model and numerical calculation method of this option.The least squares Monte Carlo approach proposed by Longstaff and Schwartz in 2001 has considerable advantages in pricing American options.Therefore,this thesis studied the problem of pricing American-style Double Barrier Parisian Call Option based on the least squares Monte Carlo approach.Firstly,a set of state variables in the pricing model of American-style Double Barrier Parisian Option are constructed to represent the triggering state of American-style Double Barrier Parisian Option,and the sub-nodes are indexed.Secondly,based on the least squares Monte Carlo approach,the pricing algorithms of classical American options and American-style Double Barrier Parisian Call Option were designed.Then,on the premise that the path of underlying asset price movement obeys the Geometric Brownian Motion,Variance Gamma process and Normal Inverse Gaussian process,option pricing was carried out.We discussed the relationship between American Option and American-style Double Barrier Parisian Call Option,and the effect of barrier width and strike price change on the price of the American-style Double Barrier Parisian Call Option was also discussed.By changing the barrier width and window length,this thesis explored the changes in the price of American-style Double Barrier Parisian Call Option.Finally,by discussing the convergence and computational efficiency of least squares Monte Carlo approach,the model was evaluated and the prospects were given.The result of this thesis states that the American-style Double Barrier Parisian Call Option is valuable before it is knocked out.The price of an American-style Double Barrier Parisian Call Option is always less than the price of corresponding American Option because of the risk of being knocked out.We find that geometric Geometric Brownian Motion and Normal Inverse Gaussian process have advantages in describing the path of underlying asset price movement,and have better simulation results.There is a positive relationship between barrier width and window length and the price of American-style Double Barrier Parisian Call Option,while the executive price has a reverse relationship with the price of American-style Double Barrier Parisian Call Option,which makes the option change from in-the-money to out-of-money.NIG process has relative advantages over VG processes in computational accuracy.In the study of computational efficiency,increasing the number of periods can more accurately depict the actual situation of price changes because the price of underlying assets is more discrete.Moreover,increasing the number of path simulation and periods makes the increment of running time of least squares Monte Carlo approach appear concave growth.The time-consuming difference of three kinds of stochastic processes is not big,and the calculation time of NIG process is the shortest and the efficiency is the highest.Compared with the classical American option,the introduction of American-style Parisian Option ensures that it can not only help shareholders save costs effectively,but also encourage executives to improve their management level,create greater value for enterprises and achieve win-win situation.