Achieving Higher Order Convergence for the Prices of European Options in Binomial Trees
Mark S. Joshi
University of Melbourne - Centre for Actuarial Studies
Mathematical Finance, Vol. 20, Issue 1, pp. 89-103, January 2010
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.
Number of Pages in PDF File: 15Accepted Paper Series
Date posted: January 18, 2010
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