A Study of Inaction in Investment Games via the Early Exercise Premium Representation

2006 ◽  
Author(s):  
Doriana Ruffino ◽  
Jonathan Treussard
Keyword(s):  
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.

scholarly journals Semimartingale Local Time and the American Put Option

2006 ◽  
Vol 13 (2) ◽  
pp. 199-214
Author(s):  
Petre Babilua
Keyword(s):  
Local Time ◽  
One Dimensional ◽  
Early Exercise ◽  
American Put Option ◽  
Put Option ◽  
A Value ◽  
Continuous Semimartingale ◽  
American Put ◽  
Semimartingale Local Time ◽  
Early Exercise Premium

Abstract A new result is obtained on the vanishing of the local time of a non-negative continuous semimartingale at zero. Based on this result, an early exercise premium representation of a value function of the American put option is obtained in a one-dimensional general diffusion model.

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

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.

MATHEMATICAL PROPERTIES OF AMERICAN CHOOSER OPTIONS

2018 ◽  
Vol 21 (08) ◽  
pp. 1850062
Author(s):  
SHI QIU ◽  
SOVAN MITRA
Keyword(s):  
Numerical Experiments ◽  
Value Function ◽  
Global Financial Crisis ◽  
Nonlinear Integral Equations ◽  
Early Exercise ◽  
Mathematical Properties ◽  
Solution Pair ◽  
Change Of Variable ◽  
The Global Financial Crisis ◽  
Early Exercise Premium

The American chooser option is a relatively new compound option that has the characteristic of offering exceptional risk reduction for highly volatile assets. This has become particularly significant since the start of the global financial crisis. In this paper, we derive mathematical properties of American chooser options. We show that the two optimal stopping boundaries for American chooser options with finite horizon can be characterized as the unique solution pair to a system formed by two nonlinear integral equations, arising from the early exercise premium (EEP) representation. The proof of EEP representation is based on the method of change-of-variable formula with local time on curves. The key mathematical properties of American chooser options are proved, specifically smooth-fit, continuity of value function and continuity of free-boundary among others. We compare the performance of the American chooser option against the American strangle option. We also conduct numerical experiments to illustrate our results.

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