scholarly journals Hints for an extension of the early exercise premium formula for American options

2005 ◽  
Vol 355 (1) ◽  
pp. 152-157 ◽  
Author(s):  
Hans-Peter Bermin ◽  
Arturo Kohatsu-Higa ◽  
Josep Perelló
Keyword(s):  
American Options ◽  
Early Exercise ◽  
Early Exercise Premium

THE EARLY EXERCISE PREMIUM IN AMERICAN OPTIONS BY USING NONPARAMETRIC REGRESSIONS

2018 ◽  
Vol 21 (07) ◽  
pp. 1850039
Author(s):  
WEIPING LI ◽  
SU CHEN
Keyword(s):  
Mean Square Error ◽  
Nonparametric Regression ◽  
American Options ◽  
Mean Square ◽  
Early Exercise ◽  
American Put Option ◽  
Put Option ◽  
Out Of Sample ◽  
American Put ◽  
Early Exercise Premium

The early exercise premium and the price of an American put option are evaluated by using nonparametric regression on the time to expiration, the moneyness and the volatility of underlying assets. In terms of mean square error (MSE), our nonparametric methods of American put option pricings outperform the existing classical methods for both in-the-sample (1 September 2011–31 January 2012) and out-of-sample (1 September 2012–28 February 2013) testings on the S&P 100 Index (OEX). Our methods have better predictions and more accurate approximations. The Greek letters for both the early exercise premium and the American put option are computed numerically.

LAPLACE BOUNDS APPROXIMATION FOR AMERICAN OPTIONS

2020 ◽  
pp. 1-34
Author(s):  
Jingtang Ma ◽  
Zhenyu Cui ◽  
Wenyuan Li
Keyword(s):  
Diffusion Process ◽  
Upper Bound ◽  
American Options ◽  
Laplace Transforms ◽  
American Option ◽  
Barrier Option ◽  
Lower And Upper Bounds ◽  
Early Exercise ◽  
The Laplace Transform ◽  
Early Exercise Premium

In this paper, we develop the lower–upper-bound approximation in the space of Laplace transforms for pricing American options. We construct tight lower and upper bounds for the price of a finite-maturity American option when the underlying stock is modeled by a large class of stochastic processes, e.g. a time-homogeneous diffusion process and a jump diffusion process. The novelty of the method is to first take the Laplace transform of the price of the corresponding “capped (barrier) option” with respect to the time to maturity, and then carry out optimization procedures in the Laplace space. Finally, we numerically invert the Laplace transforms to obtain the lower bound of the price of the American option and further utilize the early exercise premium representation in the Laplace space to obtain the upper bound. Numerical examples are conducted to compare the method with a variety of existing methods in the literature as benchmark to demonstrate the accuracy and efficiency.

WORST-CASE SCENARIOS FOR AMERICAN OPTIONS

2000 ◽  
Vol 03 (01) ◽  
pp. 25-58
Author(s):  
ROBERT BUFF
Keyword(s):  
Computational Complexity ◽  
Parameter Space ◽  
American Options ◽  
Worst Case ◽  
Knock Out ◽  
Early Exercise ◽  
Pricing Options ◽  
Diffusion Parameters ◽  
Volatility Models ◽  
Compute Time

One approach to cope with uncertain diffusion parameters when pricing options portfolios is to identify the parameters [Formula: see text] in a subset [Formula: see text] of the parameter space which form the worst-case for a particular portfolio. For the sell-side, this leads to a nonlinear algorithm that maximizes the expected liability under the risk-neutral measure. [Formula: see text] depends on the portfolio under consideration. Moreover, the algorithm must take into account that the exposure to [Formula: see text]-risk changes when non-vanilla components such as barrier or American options knock out or are exercised early. In this paper, we describe techniques to price portfolios with American options under worst-case scenarios based on uncertain volatility models. We also present heuristics which reduce the computational complexity that arises from the necessity to consider many early exercise combinations at a time. These heuristics reduce the compute time by almost one half.

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