Convergence of Finite Element Methods for Barrier Option Pricing
The barrier option is related to paths,and its pricing is more complicated.To option pricing,the most commonly numerical methods are binomial tree method,finite difference method and finite element method.In this paper,we take the European down-and-out call option as an example.In particular,we show the explicit finite difference form,and discuss the interrelationship of these three numerical methods.Furthermore,we show that,as the number of periods n tends to infinity,in the case of the European barrier call option,the finite element price converges to the Black-Scholes price at the rate of 1/√n.At the same time,we give formulas for the coefficients of 1/√n and 1/n in the expansion of the error.In addition,one numerical example is provided to validate the theoretical results.
barrier option pricingfinite element methodbinomial tree methodfinite difference methodBlack-Scholes Model
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