scholarly journals Comparison of Numerical and Analytical Approximations of the Early Exercise Boundary of the American Put Option

2010 ◽  
Author(s):  
Martin Lauko ◽  
Daniel Sevcovic
Keyword(s):  
Early Exercise ◽  
American Put Option ◽  
Put Option ◽  
Analytical Approximations ◽  
Exercise Boundary ◽  
Early Exercise Boundary ◽  
American Put

scholarly journals COMPARISON OF NUMERICAL AND ANALYTICAL APPROXIMATIONS OF THE EARLY EXERCISE BOUNDARY OF AMERICAN PUT OPTIONS

2010 ◽  
Vol 51 (4) ◽  
pp. 430-448 ◽  
Author(s):  
M. LAUKO ◽  
D. ŠEVČOVIČ
Keyword(s):  
Numerical Scheme ◽  
Analytical Approximation ◽  
Approximation Formula ◽  
Put Options ◽  
Early Exercise ◽  
Analytical Approximations ◽  
American Put Options ◽  
Exercise Boundary ◽  
Early Exercise Boundary ◽  
American Put

AbstractWe present qualitative and quantitative comparisons of various analytical and numerical approximation methods for calculating a position of the early exercise boundary of American put options paying zero dividends. We analyse the asymptotic behaviour of these methods close to expiration, and introduce a new numerical scheme for computing the early exercise boundary. Our local iterative numerical scheme is based on a solution to a nonlinear integral equation. We compare numerical results obtained by the new method to those of the projected successive over-relaxation method and the analytical approximation formula recently derived by Zhu [‘A new analytical approximation formula for the optimal exercise boundary of American put options’, Int. J. Theor. Appl. Finance9 (2006) 1141–1177].

Double barrier American put option pricing under uncertain volatility model

2021 ◽  
pp. 2150038
Author(s):  
El Kharrazi Zaineb ◽  
Saoud Sahar ◽  
Mahani Zouhir
Keyword(s):  
Single Point ◽  
Option Prices ◽  
Double Barrier ◽  
Early Exercise ◽  
Put Option ◽  
Volatility Model ◽  
Uncertain Volatility ◽  
Exercise Boundary ◽  
Early Exercise Boundary ◽  
American Style

This paper aims to study the asymptotic behavior of double barrier American-style put option prices under an uncertain volatility model, which degenerates to a single point. We give an approximation of the double barrier American-style option prices with a small volatility interval, expressed by the Black–Scholes–Barenblatt equation. Then, we propose a novel representation for the early exercise boundary of American-style double barrier options in terms of the optimal stopping boundary of a single barrier contract.

CALCULATING THE EARLY EXERCISE BOUNDARY OF AMERICAN PUT OPTIONS WITH AN APPROXIMATION FORMULA

2007 ◽  
Vol 10 (07) ◽  
pp. 1203-1227 ◽  
Author(s):  
SONG-PING ZHU ◽  
ZHI-WEI HE
Keyword(s):  
Approximation Formula ◽  
Computational Accuracy ◽  
Put Options ◽  
Early Exercise ◽  
Analytical Approximations ◽  
American Put Options ◽  
Highly Nonlinear ◽  
Exercise Boundary ◽  
Early Exercise Boundary ◽  
Long Lifetime

Accurately as well as efficiently calculating the early exercise boundary is the key to the highly nonlinear problem of pricing American options. Many analytical approximations have been proposed in the past, aiming at improving the computational efficiency and the easiness of using the formula, while maintaining a reasonable numerical accuracy at the same time. In this paper, we shall present an approximation formula based on Bunch and Johnson's work [6]. After clearly pointing out some errors in Bunch and Johnson's paper [6], we will propose an improved approximation formula that can significantly enhance the computational accuracy, particularly for options of long lifetime.

THE EARLY EXERCISE PREMIUM IN AMERICAN OPTIONS BY USING NONPARAMETRIC REGRESSIONS

2018 ◽  
Vol 21 (07) ◽  
pp. 1850039
Author(s):  
WEIPING LI ◽  
SU CHEN
Keyword(s):  
Mean Square Error ◽  
Nonparametric Regression ◽  
American Options ◽  
Mean Square ◽  
Early Exercise ◽  
American Put Option ◽  
Put Option ◽  
Out Of Sample ◽  
American Put ◽  
Early Exercise Premium

The early exercise premium and the price of an American put option are evaluated by using nonparametric regression on the time to expiration, the moneyness and the volatility of underlying assets. In terms of mean square error (MSE), our nonparametric methods of American put option pricings outperform the existing classical methods for both in-the-sample (1 September 2011–31 January 2012) and out-of-sample (1 September 2012–28 February 2013) testings on the S&P 100 Index (OEX). Our methods have better predictions and more accurate approximations. The Greek letters for both the early exercise premium and the American put option are computed numerically.

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