Characteristic Finite Element Method For Pricing Problems Of American Options And Convertible Bonds

Along with the development of the financial market in China,more and more investors began to buy stocks,securities,options,convertible bonds Securities and other types of financial products,therefore,options,bonds and other financial products pricing problems gradually become the one of the frontier problems of finance and financial mathematics study.In this paper,the first question studied is the American option on two underlying assets,studies the pricing of a put option,firstly,the Black-Scholes equation is used to establish the differential equation of the pricing problem,the linear complementarity problem of the pricing problem is written out.By introducing the penalty function,the inequality problem satisfied by the pricing problem is converted into an equation,the first derivative terms of time and space of the equation are discretized along the characteristic lines,establish the discrete approximation format,finally,the error estimates of the optimal order of 2and 1norm of the characteristic finite element solutions are given.The numerical results and error analysis show that this method overcome the numerical oscillation phenomenon,has good stability and convergence,with the correlation of two underlying assets coefficient increases gradually,volatility gradually become smaller,the gap between computing grid progressively hours,error became smaller,the order of convergence increases gradually,it is more suitable to use the characteristics of finite element method to calculate the problem.In this paper,the second problem is the study of the convertible bonds pricing problem,first by the stock follows geometric Brown motion,interest rate obey - model and risk-free arbitrage principle,A twofactor convertible bond model based on stock price and interest rate is derived,write full discrete format with characteristic finite element method and give numerical example,a numerical example shows that as the convertible bond maturity and the coupon value+ became smaller,the share price volatility 1increase gradually,the error gradually become smaller,the error convergence order gradually increase,so the characteristic finite element method is applied to estimate a convertible bond is very effective.