scholarly journals Analysis of the optimal exercise boundary of American put options with delivery lags

2021 ◽  
pp. 124916
Author(s):  
Gechun Liang ◽  
Zhou Yang
Keyword(s):  
Put Options ◽  
Optimal Exercise Boundary ◽  
American Put Options ◽  
Exercise Boundary ◽  
American Put

scholarly journals A NEW ANALYTICAL APPROXIMATION FORMULA FOR THE OPTIMAL EXERCISE BOUNDARY OF AMERICAN PUT OPTIONS

2006 ◽  
Vol 09 (07) ◽  
pp. 1141-1177 ◽  
Author(s):  
SONG-PING ZHU
Keyword(s):  
Differential Equations ◽  
Moving Boundary ◽  
Analytical Formula ◽  
Terminal Condition ◽  
Approximation Formula ◽  
Put Options ◽  
Optimal Exercise Boundary ◽  
American Put Options ◽  
Exercise Boundary ◽  
American Put

In this paper, a new analytical formula as an approximation to the value of American put options and their optimal exercise boundary is presented. A transform is first introduced to better deal with the terminal condition and, most importantly, the optimal exercise price which is an unknown moving boundary and the key reason that valuing American options is much harder than valuing its European counterparts. The pseudo-steady-state approximation is then used in the performance of the Laplace transform, to convert the systems of partial differential equations to systems of ordinary differential equations in the Laplace space. A simple and elegant formula is found for the optimal exercise boundary as well as the option price of the American put with constant interest rate and volatility. Other hedge parameters as the derivatives of this solution are also presented.

scholarly journals COMPARISON OF NUMERICAL AND ANALYTICAL APPROXIMATIONS OF THE EARLY EXERCISE BOUNDARY OF AMERICAN PUT OPTIONS

2010 ◽  
Vol 51 (4) ◽  
pp. 430-448 ◽  
Author(s):  
M. LAUKO ◽  
D. ŠEVČOVIČ
Keyword(s):  
Numerical Scheme ◽  
Analytical Approximation ◽  
Approximation Formula ◽  
Put Options ◽  
Early Exercise ◽  
Analytical Approximations ◽  
American Put Options ◽  
Exercise Boundary ◽  
Early Exercise Boundary ◽  
American Put

AbstractWe present qualitative and quantitative comparisons of various analytical and numerical approximation methods for calculating a position of the early exercise boundary of American put options paying zero dividends. We analyse the asymptotic behaviour of these methods close to expiration, and introduce a new numerical scheme for computing the early exercise boundary. Our local iterative numerical scheme is based on a solution to a nonlinear integral equation. We compare numerical results obtained by the new method to those of the projected successive over-relaxation method and the analytical approximation formula recently derived by Zhu [‘A new analytical approximation formula for the optimal exercise boundary of American put options’, Int. J. Theor. Appl. Finance9 (2006) 1141–1177].

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