Convergence of European Lookback Options with Floating Strike in the Binomial Model

TL;DR

This paper analyzes the convergence rate of European lookback options with floating strike in the binomial model to their Black-Scholes prices, providing precise error terms and extending to delta calculations.

Contribution

It offers a detailed convergence analysis with explicit error terms for the binomial approximation of lookback options, including delta, using an improved lemma and double sum representation.

Findings

Convergence rate of order 1/√n for option price and delta.

Explicit formulas for the leading error term in the binomial approximation.

Extension of error analysis to cases with non-zero risk-free interest rate.

Abstract

In this article we study the convergence of a European lookback option with floating strike evaluated with the binomial model of Cox-Ross-Rubinstein to its evaluation with the Black-Scholes model. We do the same for its delta. We confirm that these convergences are of order 1/Sqrt(n). For this, we use the binomial model of Cheuk-Vorst which allows us to write the price of the option using a double sum. Based on an improvement of a lemma of Lin-Palmer, we are able to give the precise value of the term in 1/Sqrt(n) in the expansion of the error; we also obtain the value of the term in 1/n if the risk free interest rate is non zero. This modelisation will also allow us to determine the first term in the expansion of the delta.