scholarly journals On a Numerical Approximation Scheme for Construction of the Early Exercise Boundary for a Class of Nonlinear Black-Scholes Equations

2010 ◽  
Author(s):  
Daniel Sevcovic
Keyword(s):  
Numerical Approximation ◽  
Approximation Scheme ◽  
Early Exercise ◽  
Black Scholes ◽  
Exercise Boundary ◽  
Early Exercise Boundary

scholarly journals Early Exercise Decision in American Options with Dividends, Stochastic Volatility, and Jumps

2018 ◽  
Vol 55 (1) ◽  
pp. 331-356 ◽  
Author(s):  
Antonio Cosma ◽  
Stefano Galluccio ◽  
Paola Pederzoli ◽  
Olivier Scaillet
Keyword(s):  
Stochastic Volatility ◽  
Opportunity Cost ◽  
Numerical Technique ◽  
Large Database ◽  
Early Exercise ◽  
Black Scholes ◽  
Correct Calculation ◽  
Exercise Boundary ◽  
Early Exercise Boundary ◽  
Transaction Fees

Using a fast numerical technique, we investigate a large database of investors’ suboptimal nonexercise of short-maturity American call options on dividend-paying stocks listed on the Dow Jones. The correct modeling of the discrete dividend is essential for a correct calculation of the early exercise boundary, as confirmed by theoretical insights. Pricing with stochastic volatility and jumps instead of the Black–Scholes–Merton benchmark cuts the amount lost by investors through suboptimal exercise by one-quarter. The remaining three-quarters are largely unexplained by transaction fees and may be interpreted as an opportunity cost for the investors to monitor optimal exercise.

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.

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