Based On Optimal Exercise Boundary Of American Option Pricing's Numerical Simulation And Analysis

Financial mathematics makes use of the modern mathematics theories and methods to qualitatively and quantitatively study financial theory and practice. Financial derivative is a kind of risk management tool, and its price depends on the change of asset prices. Option is the best important financial derivative. Option gives the holder a certain time in the future to determine the price to buy or sell an underlying asset rights. Option pricing is the core of Option theory, for the European option, Black--Scholes had given an analytical form of the pricing formula. However, there is no analytical formula for American options pricing, and it can't obtain the exact solutions. Therefore, it is important to study the method of American option pricing.This paper mainly studies the numerical simulation of the valuation of American put options and the American Call Option based on the optimal exercise boundary. And its Key research is on the numerical calculation of the optimal exercise boundary which is applied to nonlinear second Volterra integral equation. Then it proposed three numerical schemes about the optimal exercise boundary of American options: composite trapezoidal form, and composite right rectangular format and composite left rectangular format. The numerical experiments on the three proposed format of the numerical analysis and comparison proved that composite trapezoidal format has the highest precision and this format can be used to solve the valuation of American put options and the American Call Option and the numerical simulation.