The Theoryand Implemention Ofamerican Options Valuation Using LSM Simulation Based On GARCH Model

Inorder to price options which have the possibility of early exercise, usual techniques are Least Squaeres Montecarlo simulation, tree methods and PDE methods. To avoid the storage and computation grows exponentially in the number of dimentions, the LSM method is a better choice. Simply use constant historical volatility of option price cause mispricing, so this paper establish the GARCH(1,1) framework to discribe the volatility, and taking into account dividends, transaction costs and other factors, to accurately the volatility and provide the conditions for option pricing.paper first discusses the main research methods of American option pricing and analysis of LSM option pricing research status, as later theoretical groundwork. The Chapter Two is the studies of financial time series volatility, including a description of GARCH model and parameter estimation, the common function of financial time series in MATLAB, and empirical stock returns'distribution whether obey the GARCH framework, numerical results fit the theoretical results. Chapter three, give the systematic theoretical studies on the LSM methods pricing American options, including single assets and multi-asset American option pricing research, then summed up the pricing modeling idea, according to the thread, empirical single dimensional, multi-dimensional American-based GARCH option pricing. Here multi-dimensional American options mainly refers to max options and basket options.To make the application of previous theoretical results more easily and widely, Chapter Four create GUI interface in MATLAB, and gives the details code to achieve the control functions in order to making pricing system, then make this "System of American options Valuation using LSM simulation based on GARCH model " into .exe file, in this way, the computer not installed MATLAB can also use this system. Finally, Chapter Five in this paper, to detect the utility and accuracy of the system,do empirical test with the actual data in the Hong Kong Stock Exchang, and propose practical value of stock options.