scholarly journals Employee Stock Option Valuation with an Early Exercise Boundary

2008 ◽  
Vol 64 (5) ◽  
pp. 88-100 ◽  
Author(s):  
Neil Brisley ◽  
Chris K. Anderson
Keyword(s):  
Stock Option ◽  
Option Valuation ◽  
Early Exercise ◽  
Employee Stock Option ◽  
Exercise Boundary ◽  
Early Exercise Boundary

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.

scholarly journals The Early Exercise Boundary Under the Jump to Default Extended CEV Model

2018 ◽  
Vol 82 (1) ◽  
pp. 151-181 ◽  
Author(s):  
João Pedro Vidal Nunes ◽  
José Carlos Dias ◽  
João Pedro Ruas
Keyword(s):  
Cev Model ◽  
Early Exercise ◽  
Exercise Boundary ◽  
Early Exercise Boundary

scholarly journals Bootstrapping the Early Exercise Boundary in the Least-Squares Monte Carlo Method

2019 ◽  
Vol 12 (4) ◽  
pp. 190 ◽  
Author(s):  
Pascal Létourneau ◽  
Lars Stentoft
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
American Option Pricing ◽  
Cross Sectional ◽  
Early Exercise ◽  
Backwards Induction ◽  
Simulation Based ◽  
Multiple Cross ◽  
Exercise Boundary ◽  
Early Exercise Boundary

This paper proposes an innovative algorithm that significantly improves on the approximation of the optimal early exercise boundary obtained with simulation based methods for American option pricing. The method works by exploiting and leveraging the information in multiple cross-sectional regressions to the fullest by averaging the individually obtained estimates at each early exercise step, starting from just before maturity, in the backwards induction algorithm. With this method, less errors are accumulated, and as a result of this, the price estimate is essentially unbiased even for long maturity options. Numerical results demonstrate the improvements from our method and show that these are robust to the choice of simulation setup, the characteristics of the option, and the dimensionality of the problem. Finally, because our method naturally disassociates the estimation of the optimal early exercise boundary from the pricing of the option, significant efficiency gains can be obtained by using less simulated paths and repetitions to estimate the optimal early exercise boundary than with the regular method.

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