scholarly journals Pricing American Options under Stochastic Volatility: A New Method Using Chebyshev Polynomials to Approximate the Early Exercise Boundary

2003 ◽  
Author(s):  
Elias Tzavalis ◽  
Shijun Wang
Keyword(s):  
Stochastic Volatility ◽  
Chebyshev Polynomials ◽  
American Options ◽  
New Method ◽  
Early Exercise ◽  
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.

ALTERNATIVE RANDOMIZATION FOR VALUING AMERICAN OPTIONS

2010 ◽  
Vol 27 (02) ◽  
pp. 167-187 ◽  
Author(s):  
TOSHIKAZU KIMURA
Keyword(s):  
Numerical Experiments ◽  
Recursive Algorithm ◽  
American Options ◽  
Random Variable ◽  
Option Value ◽  
Early Exercise ◽  
Maturity Date ◽  
Exercise Boundary ◽  
Early Exercise Boundary ◽  
Randomization Method

This paper deals with randomization methods for valuing American options written on dividend-paying assets, which are based on the idea of treating the maturity date as a random variable. In the randomization method introduced by Carr in 1998, he used the Erlangian distributed random variable to develop a recursive algorithm starting from the so-called Canadian option with an exponentially distributed random maturity. The purposes of this paper are (i) to provide much simpler pricing formulas for the Canadian option; (ii) to interpret the Gaver–Stehfest method developed for inverting Laplace transforms as an alternative randomization method in the context of valuing American options; and (iii) to evaluate the performance of the Gaver–Stehfest method in details with theoretical and numerical views. Numerical experiments indicate that the Gaver–Stehfest method works well to generate accurate approximations for the early exercise boundary as well as the option value.

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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