Richardson Extrapolation Of Finite Element Methods For Option Pricing

In the wake of the rapid development of financial market, a large variety of financial derivatives have been designed. In recent decade, financial derivatives have formed a market and exerted significant influence on global economy. Options, especially, obtain more and more attention from the people. This is because it has the excellent function of avoiding risk, risk investment and value identification, and demonstrates the characteristics of flexibility and diversity. Options are the core instrument for risk management. So, it is necessary to probe into option. The former scholar did it. In1973, Fischer Black and Myron Scholes won the Nobel Prize because of establishing the call option pricing formula. Although for European option pricing the closed-form solutions do exist, with the computation power we enjoy nowadays, numerical methods are often preferred. The binomial tree method, the finite difference method and the finite element method are the most commonly used numerical method in option pricing.In this paper, we show that the relationship between the three numerical methods and use these relationship describing the case of a European call option the finite element price converges to the Black-Scholes price at the rate of1/n as the number of periods n tends to infinity, and give a formula for the coefficient of1/n in the expansion of the error. In addition, two numerical examples are provided to validate the theoretical results.