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.

scholarly journals Measure of Similarity between GMMs by Embedding of the Parameter Space That Preserves KL Divergence

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 957
Author(s):  
Branislav Popović ◽  
Lenka Cepova ◽  
Robert Cep ◽  
Marko Janev ◽  
Lidija Krstanović
Keyword(s):  
Computational Complexity ◽  
Parameter Space ◽  
Recognition Accuracy ◽  
Gaussian Mixture Models ◽  
Gaussian Mixture ◽  
Dimensional Manifold ◽  
Dimensional Parameter ◽  
Trade Off ◽  
Measure Of Similarity ◽  
Lower Dimensional

In this work, we deliver a novel measure of similarity between Gaussian mixture models (GMMs) by neighborhood preserving embedding (NPE) of the parameter space, that projects components of GMMs, which by our assumption lie close to lower dimensional manifold. By doing so, we obtain a transformation from the original high-dimensional parameter space, into a much lower-dimensional resulting parameter space. Therefore, resolving the distance between two GMMs is reduced to (taking the account of the corresponding weights) calculating the distance between sets of lower-dimensional Euclidean vectors. Much better trade-off between the recognition accuracy and the computational complexity is achieved in comparison to measures utilizing distances between Gaussian components evaluated in the original parameter space. The proposed measure is much more efficient in machine learning tasks that operate on large data sets, as in such tasks, the required number of overall Gaussian components is always large. Artificial, as well as real-world experiments are conducted, showing much better trade-off between recognition accuracy and computational complexity of the proposed measure, in comparison to all baseline measures of similarity between GMMs tested in this paper.

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 The computational complexity of the parallel knock-out problem

2008 ◽  
Vol 393 (1-3) ◽  
pp. 182-195 ◽  
Author(s):  
Hajo Broersma ◽  
Matthew Johnson ◽  
Daniël Paulusma ◽  
Iain A. Stewart
Keyword(s):  
Computational Complexity ◽  
Knock Out

Pricing American Options under the Constant Elasticity of Variance Model and Subject to Bankruptcy

2009 ◽  
Vol 44 (5) ◽  
pp. 1231-1263 ◽  
Author(s):  
João Pedro Vidal Nunes
Keyword(s):  
American Options ◽  
Asymptotic Properties ◽  
Variance Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Early Exercise ◽  
Exercise Boundary ◽  
And Diffusion

AbstractThis paper proposes an alternative characterization of the early exercise premium that is valid for any Markovian and diffusion underlying price process as well as for any parameterization of the exercise boundary. This new representation is shown to provide the best pricing alternative available in the literature for medium- and long-term American option contracts, under the constant elasticity of variance model. Moreover, the proposed pricing methodology is also extended easily to the valuation of American options on defaultable equity and possesses appropriate asymptotic properties.

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