Achieving Higher Order Convergence for the Prices of European Options in Binomial Trees
نویسنده
چکیده
A new family of binomial trees as approximations to the Black–Scholes model is introduced. For this class of trees, the existence of complete asymptotic expansions for the prices of vanilla European options is demonstrated and the first three terms are explicitly computed. As special cases, a tree with third order convergence is constructed and the conjecture of Leisen and Reimer that their tree has second order convergence is proven.
منابع مشابه
Achieving Smooth Asymptotics for the Prices of European Options in Binomial Trees
A new binomial approximation to the Black–Scholes model is introduced. It is shown that for digital options and vanilla European call and put options that a complete asymptotic expansion of the error in powers of n−1 exists. This is the first binomial tree for which such an asymptotic expansion has been shown to exist.
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