Approximate solutions for the British put option and its optimal exercise boundary

2016 ◽  
Vol 57 ◽  
pp. 222
Author(s):  
Joanna Goard
Keyword(s):  
Approximate Solutions ◽  
Optimal Exercise Boundary ◽  
Put Option ◽  
Exercise Boundary

APPROXIMATE SOLUTIONS FOR THE BRITISH PUT OPTION AND ITS OPTIMAL EXERCISE BOUNDARY

2016 ◽  
Vol 57 (3) ◽  
pp. 222-243
Author(s):  
JOANNA GOARD
Keyword(s):  
Stock Price ◽  
Approximate Solutions ◽  
Financial Derivatives ◽  
Put Options ◽  
Early Exercise ◽  
Empirical Results ◽  
Analytic Approximations ◽  
Optimal Exercise Boundary ◽  
Put Option ◽  
Exercise Boundary

British put options are financial derivatives with an early exercise feature whereby on payoff, the holder receives the best prediction of the European put payoff under the hypothesis that the true drift of the stock price is equal to a contract drift. In this paper, we derive simple analytic approximations for the optimal exercise boundary and the option valuation, valid for short expiry times – which is a common feature of most options traded in the market. Empirical results show that the approximations provide accurate results for expiries of at least up to two months.

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 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.

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.

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