Optimal Early Exercise of Vulnerable American Options

2009 ◽  
Author(s):  
Peter Charles Klein
Keyword(s):  
American Options ◽  
Early Exercise

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.

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.

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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