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The rate of convergence of the binomial tree scheme

Abstract. We study the detailed convergence of the binomial tree scheme. It is known that the scheme is first order. We find the exact constants, and show it is possible to modify Richardson extrapolation to get a method of order three-halves. We see that the delta, used in hedging, converges at the same rate. We analyze this by first embedding the tree scheme in the Black-Scholes diffusion model by means of Skorokhod embedding. We remark that this technique applies to much more general cases.

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Manuscript received: February 2001; final version received: August 2002

I would like to thank O. Walsh for suggesting this problem and for many helpful conversations.

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Walsh, J. The rate of convergence of the binomial tree scheme. Finance Stochast 7, 337–361 (2003).

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  • Key words: Tree scheme, options, rate of convergence, Skorokhod embedding
  • JEL Classification: G13
  • Mathematics Subject Classification (1991): 91B24, 60G40, 60G44