Calculation Of The Upper And Lower Bounds Of American Options Based On Interest Rate Term Structure By Simulation

Today,finance has become an indispensable area in people's lives.Everyone has been in constant contact with various financial institutions such as banks,insurance,and securities since birth.In particular,every outbreak of the financial crisis will affect the hearts of hundreds of millions of people and bring a huge impact to the entire national economy.Tracing back to the source,the financial industry can have a vigorous development and a pivotal position today,is in fact inseparable from the two Wall Street revolutions of the 20th century.It is these two revolutions that have made the financial market begin to advance in the direction of quantificationWith the advent of the first Wall Street revolution,finance began to enter people's attention.The introduction of the Markowitz mean-variance model began to give the theoretical interpretation and expression of the real financial market,and it has become an important guiding basis for the study of investment portfolio issues,and it has been passed down to the presentIf the first Wall Street revolution was the beginning of modern financial development,then the second Wall Street revolution marked by the birth of the Black-Scholes formula was another leap in the modern financial industry.It has made the derivatives market gradually become an important part of the financial market,and has greatly improved the hedging function of the financial marketThe advancement of theory leads to the innovation of practice,and the innovation of practice turns to the continuous development and improvement of the theory.The formulation of the B-S formula makes the pricing of various European options have a theoretical basis,but this does not solve the pricing problem of American options.In fact,the particularity of the American option itself leads to no theoretically explicit solution to its price.As a result,the Monte Carlo stochastic simulation began to be on the financial stage as a powerful tool for solving such problems.Through random simulation,the pricing of many options and other derivatives can be solved,including the upper and lower bounds of American optionsThis paper first introduces the basic knowledge about options,and on this basis,it focuses on the main features and theoretical pricing models of American options.In the application of stochastic simulation to solve the American option pricing problem,the basic ideas of the random tree method,the stochastic mesh method and the regression-based method and the determination of two kinds of estimators are introduced.After that,the upper and lower bounds of the value of American options are simulated by using random tree and stochastic mesh under the assumption that stock price follows geometric Brownian motion,and the assumption that the risk-free interest rate is fixed in these methods is relaxed to some extent.Based on the introduction of the stochastic interest rate model,the relationship between stock price and risk-free interest rate is determined by economic theory and market data,and then calculated the upper and lower bounds of American option value based on stocks to make the simulation results closer to the real market.