Rate of convergence for discrete approximation of option prices

TL;DR

This paper analyzes how quickly discrete models approximate option prices, providing explicit error formulas and demonstrating convergence rates, especially for binomial to Black-Scholes models, including smooth convergence scenarios.

Contribution

It introduces a method to derive explicit error formulas for general options based on digital option prices and studies convergence rates for binomial approximations to Black-Scholes prices.

Findings

Explicit error formulas for option price approximation

Convergence rates for binomial to Black-Scholes models

Conditions for smooth, non-oscillatory convergence

Abstract

In this article, we study the rate of convergence of prices when a model is approximated by some simplified model. We also provide a method how explicit error formula for more general options can be obtained if such formula is available for digital option prices. We illustrate our results by considering convergence of binomial prices to Black-Scholes prices. We also consider smooth convergence in which the approximation does not oscillate for general class of payoff functions.