Pricing the American put option: a detailed convergence analysis for binomial models

Leisen and Reimer (1996) suggested to consider the order of convergence as a measure of convergence speed for European call options. In this paper we study in a first step the problem of determining the order of convergence in pricing American put options for several approaches in the literature. We will then examine in detail extrapolation and the Control Variate technique for improving convergence and will explain their pitfalls. Since the investigation reveals the need for smooth converging models in order to get smaller initial errors, such a model is constructed. The different approaches are then tested: simulations exhibit up to 100 times smaller initial errors. � 1998 Published by Elsevie

Pricing the American put option: a detailed convergence analysis for binomial models

SIGLEAvailable from Bibliothek des Instituts fuer Weltwirtschaft, ZBW, D-21400 Kiel W 109 (366) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Stock Evolution under Stochastic Volatility: A Discrete Approach

This paper examines the pricing of options by approximating extensions of the Black--Scholes setup in which volatility follows a separate diffusion process. It generalizes the well--known binomial model, constructing a discrete two-- dimensional lattice. We discuss convergence issues extensively and calculate prices and implied volatilities for European-- and American--style put options. Keywords binomial model, option valuation, lattice approach, stochastic volatility JEL Classification G13 Stanford University, Hoover Institution, Stanford, CA 94305, U.S.A. email: [email protected] A Deutscher Akademischer Austauschdienst scholarship through HSP III (a joint program by the Federal and State Governments in Germany) is gratefully acknowledged. 1 Introduction In the setup of Samuelson (1965), Black and Scholes removed the intrinsic risk in a call option by continuous trading in the underlying stock and one bond; this has been the starting point for today's industry of pri..