scholarly journals Closed Form Optimal Exercise Boundary of the American Put Option

2020 ◽  
Author(s):  
Yerkin Kitapbayev
Keyword(s):  
Closed Form ◽  
American Put Option ◽  
Optimal Exercise Boundary ◽  
Put Option ◽  
Exercise Boundary ◽  
American Put

scholarly journals CLOSED FORM OPTIMAL EXERCISE BOUNDARY OF THE AMERICAN PUT OPTION

2021 ◽  
Vol 24 (01) ◽  
pp. 2150004
Author(s):  
YERKIN KITAPBAYEV
Keyword(s):  
Integral Equation ◽  
Closed Form ◽  
Stock Price ◽  
Time Dependent ◽  
Strike Price ◽  
American Put Option ◽  
Optimal Exercise Boundary ◽  
Put Option ◽  
Exercise Boundary ◽  
American Put

We present three models of stock price with time-dependent interest rate, dividend yield, and volatility, respectively, that allow for explicit forms of the optimal exercise boundary of the finite maturity American put option. The optimal exercise boundary satisfies the nonlinear integral equation of Volterra type. We choose time-dependent parameters of the model so that the integral equation for the exercise boundary can be solved in the closed form. We also define the contracts of put type with time-dependent strike price that support the explicit optimal exercise boundary.

Sensitivity analysis of the optimal exercise boundary of the American put option

2016 ◽  
Vol 23 (3) ◽  
pp. 429-433
Author(s):  
Nasir Rehman ◽  
Sultan Hussain ◽  
Wasim Ul-Haq
Keyword(s):  
Stock Price ◽  
Obstacle Problem ◽  
One Dimensional ◽  
American Put Option ◽  
Optimal Exercise Boundary ◽  
Put Option ◽  
Dimensional Diffusion ◽  
Exercise Boundary ◽  
American Put ◽  
Continuity Estimate

AbstractWe consider the American put problem in a general one-dimensional diffusion model. The risk-free interest rate is constant, and volatility is assumed to be a function of time and stock price. We use the well-known parabolic obstacle problem and establish the continuity estimate of the optional exercise boundaries of the American put option with respect to the local volatilities, which may be considered as a generalization of the Achdou results [1].

scholarly journals An investigation on the existence and uniqueness analysis of the optimal exercise boundary of American put option

Filomat ◽  
2021 ◽  
Vol 35 (4) ◽  
pp. 1095-1105
Author(s):  
Davood Ahmadian ◽  
Akbar Ebrahimi ◽  
Karim Ivaz ◽  
Mariyan Milev
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Banach Fixed Point Theorem ◽  
Closed Set ◽  
American Put Option ◽  
Optimal Exercise Boundary ◽  
Put Option ◽  
Exercise Boundary ◽  
American Put

In this paper, we discuss the Banach fixed point theorem conditions on the optimal exercise boundary of American put option paying continuously dividend yield, to investigate whether its existence, uniqueness, and convergence are derived. In this respect, we consider the integral representation of the optimal exercise boundary which is extracted as a consequence of the Feynman-Kac formula. In order to prove the above features, we define a nonempty closed set in Banach space and prove that the proposed mapping is contractive and onto. At final, we illustrate the ratio convergence of the mapping on the optimal exercise boundary.

scholarly journals On the optimal exercise boundary for an American put option

2001 ◽  
Vol 1 (1) ◽  
pp. 39-45 ◽  
Author(s):  
Ghada Alobaidi ◽  
Roland Mallier
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Asymptotic Expansions ◽  
American Put Option ◽  
Optimal Exercise Boundary ◽  
Put Option ◽  
Exercise Boundary ◽  
A Free Boundary Problem ◽  
The Right ◽  
American Put

An American put option is a derivative financial instrument that gives its holder the right but not the obligation to sell an underlying security at a pre-determined price. American options may be exercised at any time prior to expiry at the discretion of the holder, and the decision as to whether or not to exercise leads to a free boundary problem. In this paper, we examine the behavior of the free boundary close to expiry. Working directly with the underlying PDE, by using asymptotic expansions, we are able to deduce this behavior of the boundary in this limit.

scholarly journals A Simple Numerical Method for Pricing an American Put Option

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Beom Jin Kim ◽  
Yong-Ki Ma ◽  
Hi Jun Choe
Keyword(s):  
Free Boundary ◽  
Numerical Method ◽  
Quadratic Equation ◽  
Numerical Results ◽  
American Put Option ◽  
Optimal Exercise Boundary ◽  
Put Option ◽  
Exercise Boundary ◽  
American Put

We present a simple numerical method to find the optimal exercise boundary in an American put option. We formulate an intermediate function with the fixed free boundary that has Lipschitz character near optimal exercise boundary. Employing it, we can easily determine the optimal exercise boundary by solving a quadratic equation in time-recursive way. We also present several numerical results which illustrate a comparison to other methods.

scholarly journals A Quasi-Closed-Form Solution for the Valuation of American Put Options

2020 ◽  
Vol 8 (4) ◽  
pp. 62
Author(s):  
Cristina Viegas ◽  
José Azevedo-Pereira
Keyword(s):  
Closed Form ◽  
Method Of Lines ◽  
Closed Form Solution ◽  
Form Solution ◽  
Option Value ◽  
Put Options ◽  
American Put Option ◽  
Put Option ◽  
American Put Options ◽  
American Put

This study develops a quasi-closed-form solution for the valuation of an American put option and the critical price of the underlying asset. This is an important area of research both because of a large number of transactions for American put options on different underlying assets (stocks, currencies, commodities, etc.) and because this type of evaluation plays a role in determining the value of other financial assets such as mortgages, convertible bonds or life insurance policies. The procedure used is commonly known as the method of lines, which is considered to be a formulation in which time is discrete rather than continuous. To improve the quality of the results obtained, the Richardson extrapolation is applied, which allows the convergence of the outputs to be accelerated to values close to reality. The model developed in this paper derives an explicit formula of the finite-maturity American put option. The results obtained, besides allowing us to quickly determine the option value and the critical price, enable the graphical representation—in two and three dimensions—of the option value as a function of the other components of the model.

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