American Option Pricing Model Based On Kernel Density Estimation

With the continuous complication of the global economic situation,the economic environment is gradually being transformed and upgraded.There is no doubt that options are advantageous for risk aversion due to their convenient risk hedging,and have become one of the most popular financial derivatives.On the other hand,the option is also a speculative tool with a high degree of leverage,which can be doubled through a small amount of investment.Therefore,the development of options is of great significance for the deepening of financial reform and innovation.Options can be divided into two categories according to the difference in delivery time: European and American.The delivery time of American options is relatively flexible.Its pricing theory has received extensive attention in the financial and math fields.At the same time,the volatility of the underlying assets has a large correlation with the price of American options,but the volatility itself is unobservable.Therefore,it is a very challenging problem to consider the randomness of volatility to price American options.In 2010,Hamatani and Fukushima studied stochastic linear complementary models of American options with uncertain volatility.The models used historical volatility to replace the expectation of stochastic volatility.This paper considers volatility on the basis of its research.For the continuous random variable,the probability density function of the volatility is estimated by using the kernel density method based on the historical volatility sample data,and the American option pricing problem with uncertain volatility is studied based on this density function.This paper is based on the market historical data information.In consideration of the uncertainty of the stochastic volatility of the underlying asset,the random complementary model of American options is studied.Firstly,a series of market historical prices of the underlying assets are analyzed to obtain discrete sample set of random volatility.Based on these sample points,a weighted kernel density estimation method is used to select appropriate kernel functions and window widths to obtain stochastic volatility.The approximate density function-weighted kernel density function,from which to calculate the stochastic volatility expectations.Then based on this expectation and the stochastic linear complementarity model of American option,the nonlinear complementarity function is used to transform the deterministic linear complementarity problem into the optimization problem.Finally,a preliminary numerical experiment was conducted on the stock options of Hong Kong Stock Exchange.The numerical results show that in some cases,the results of the model are better than the results of the binomial model and are closer to the current market price.Chapter 1 briefly describes the development and current status of domestic and foreign option pricing research,pricing theory and related methods,etc.Chapter 2 briefly introduces complementary theory and its common solutions.Chapter 3 outlines the issue of the dynamic boundary of American option pricing,the theory of random complementary models,followed by the introduction of weighted kernel density estimation theory.Chapter 4 first gives an American option pricing model with stochastic volatility based on kernel density estimation,and finally gives numerical experimental results and conclusions.